Fire Rescue Victoria (FRV) Written Selection Test

A 3x3 grid contains shapes in a sequence. The top row has: a circle, a square, and a triangle. The middle row has: a square, a triangle, and a circle. The bottom row has: a triangle, a circle, and a blank space. Which shape logically completes the bottom row?

• ACircle
• BTriangle
• CSquare
• DDiamond

A sequence of four shapes is shown. The first is a triangle pointing up. The second is a square. The third is a regular pentagon pointing up. The fourth is a regular hexagon. What is the fifth shape in this sequence?

• ARegular heptagon pointing up
• BRegular octagon
• CCircle
• DPentagon pointing down

An arrow inside a circle rotates clockwise in a sequence: first pointing at 12 o'clock, then pointing at 2 o'clock, then pointing at 5 o'clock, and then pointing at 9 o'clock. Where does the arrow point in the next step?

• A11 o'clock
• B12 o'clock
• C1 o'clock
• D2 o'clock

Identify the odd one out among the following groups of lines: Group A has 4 horizontal lines. Group B has 4 vertical lines. Group C has 4 diagonal lines parallel to each other. Group D has 4 lines that intersect at a single central point.

• AGroup A
• BGroup B
• CGroup C
• DGroup D

A net of a cube is shown. It has symbols on its faces: a dot, a cross, a triangle, a square, a star, and a circle. When folded into a 3D cube, if the face with the dot is on top and the face with the cross is on the bottom, which of the following is mathematically impossible?

• AThe face with the triangle is opposite the face with the square
• BThe face with the star is opposite the face with the circle
• CThe face with the dot is adjacent to the face with the cross
• DThe face with the triangle is adjacent to the face with the star

A matrix pattern contains lines. Row 1 has 1 vertical line, 2 vertical lines, and 3 vertical lines. Row 2 has 1 horizontal line, 2 horizontal lines, and 3 horizontal lines. Row 3 has 1 diagonal line, 2 diagonal lines, and a blank space. What completes the blank space?

• A3 horizontal lines
• B3 vertical lines
• C3 diagonal lines
• D4 diagonal lines

A circle and a square intersect. In the first frame, they do not overlap. In the second frame, they overlap slightly, creating 3 distinct regions. In the third frame, the circle moves completely inside the square. How many distinct regions exist in the third frame?

• A1
• B2
• C3
• D4

A square grid contains black dots. In the first grid, there is 1 dot in the top-left. In the second, there are 2 dots: top-left and top-right. In the third, there are 3 dots: top-left, top-right, and bottom-right. If the pattern continues clockwise around the corners, where are the dots in the fourth grid?

• AAll four corners contain a dot
• BTop-left, top-right, and bottom-left
• CTop-right, bottom-right, and bottom-left
• DTop-left, bottom-right, and bottom-left

A regular hexagon contains a shaded triangle. In the first frame, the top triangle is shaded. In the second frame, the adjacent triangle to the right is shaded. In the third frame, the next triangle to the right is shaded. What describes the rotation of the shaded region?

• AClockwise rotation of 60 degrees
• BCounter-clockwise rotation of 60 degrees
• CClockwise rotation of 120 degrees
• DCounter-clockwise rotation of 120 degrees

A shape resembles the letter 'L'. In the first frame, it is upright. In the second frame, it is reflected horizontally (mirrored). In the third frame, it is flipped vertically (inverted). In the fourth frame, it is reflected horizontally again. How does the shape compare to the first frame?

• AIt is identical to the first frame
• BIt is flipped vertically (inverted) compared to the first frame
• CIt is reflected horizontally (mirrored) compared to the first frame
• DIt is rotated 90 degrees clockwise compared to the first frame

A visual addition rule states that the two input shapes are overlaid and every line from both is kept; where identical lines coincide they merge into a single line (they are not duplicated). If a square with a vertical line through the center is 'added' to a square with a horizontal line through the center, what is the resulting shape?

• AA blank square
• BA square with a cross (both vertical and horizontal lines)
• CA square with only a vertical line
• DA circle with a cross

A transparent cube is shown in different perspectives. Face A is adjacent to Faces B, C, D, and E. Face F is opposite Face A. Which face must be opposite Face B?

• AFace C
• BFace D
• CFace E
• DCannot be determined without knowing the adjacent relationships of B

A five-pointed star has one point shaded black. The shading rotates clockwise, skipping one point each time (e.g., from point 1, it skips 2 and lands on 3). If it starts at the top point (1), what is the sequence of shaded points for the first four steps?

• A1, 3, 5, 2, 4
• B1, 2, 3, 4, 5
• C1, 3, 2, 4, 5
• D1, 4, 2, 5, 3

A grid sequence has a circle that moves down 1 unit at each step, while a triangle moves right 1 unit at each step. If they start at the top-left coordinate (1,1) of a 4x4 grid, at which coordinate will they first intersect?

• A(2,2)
• B(3,3)
• C(4,4)
• DThey will never intersect

In a 3x3 matrix, the top row shows three shapes with 3, 4, and 5 sides. The second row shows shapes with 4, 5, and 6 sides. The third row starts with a shape of 5 sides, followed by a shape of 6 sides. What is the number of sides of the final shape in the third row?

• A5 sides
• B6 sides
• C7 sides
• D8 sides

A pattern consists of arrows. Arrow 1 points Up. Arrow 2 points Right. Arrow 3 points Down. Arrow 4 points Left. If this cycle repeats, what is the direction of Arrow 99?

• AUp
• BRight
• CDown
• DLeft

A square piece of paper is folded in half diagonally to form a triangle. It is then folded in half again to form a smaller triangle. A single circular hole is punched through the center of this folded triangle. When the paper is completely unfolded, how many holes will be visible?

• A2
• B4
• C6
• D8

A 3x3 matrix has shaded grids. The top row has: 1 shaded square, 2 shaded squares, 3 shaded squares. The middle row has: 2 shaded squares, 3 shaded squares, 4 shaded squares. The bottom row has: 3 shaded squares, 4 shaded squares, and a blank space. How many squares should be shaded in the blank space?

• A3
• B4
• C5
• D6

A sequence of figures consists of lines. Figure 1 has 1 line segment. Figure 2 has 3 segments (forming a triangle). Figure 3 has 5 segments (two connected triangles sharing an edge). Figure 4 has 7 segments. What is the pattern of growth in the number of segments?

• AMultiply by 2 at each step
• BIncrease by 2 at each step
• CIncrease by 1, then 2, then 3
• DDouble the previous number and subtract 1

Shape A is a square. Shape B is a square divided into 4 equal quadrants by a cross. Shape C is a circle. What is the logical analogue to Shape D?

• AA circle divided into 4 quadrants by a cross
• BA square inside a circle
• CA circle inside a square
• DAn undivided circle

A logical grid operates like an XOR gate: where lines overlap in the two input shapes, they are deleted in the output. If Input 1 is a large circle containing a small circle, and Input 2 is a large circle containing a small square, what is the output?

• AA large circle containing both the small circle and the small square
• BA blank shape
• COnly the small circle and the small square (the large circle is deleted)
• DA small circle inside a small square

A domino sequence has top and bottom numbers. Domino 1: [1/2]. Domino 2: [2/4]. Domino 3: [3/6]. Domino 4: [4/1]. (Note: domino values wrap around from 6 to 1). What is the value of Domino 5?

• A[5/2]
• B[5/3]
• C[6/2]
• D[6/3]

A sequence of polygons starts with a triangle, then a square, then a pentagon, then a hexagon. Inside each polygon, there are half as many diagonal lines as the polygon has sides (rounded down). How many diagonals are inside the hexagon?

• A2
• B3
• C4
• D5

A shape subtraction gate operates as follows: any lines present in the first shape that are also present in the second shape are removed. If Shape 1 is a square with a horizontal line and a vertical line (a cross), and Shape 2 is a vertical line, what is the output shape?

• AA square with a horizontal line
• BA square with a vertical line
• CA blank square
• DA horizontal line only

A single shaded square sits in the top-left cell of a 3x3 grid. The entire grid is rotated 90 degrees clockwise, and then rotated a further 90 degrees clockwise (a total of 180 degrees). In which cell does the shaded square end up?

• ATop-right cell
• BBottom-left cell
• CBottom-right cell
• DCenter cell

A balanced lever is 2 meters long with a central pivot. A 10 kg mass is placed 0.5 meters to the left of the pivot. What mass must be placed 1 meter to the right of the pivot to maintain static balance?

• A5 kg
• B10 kg
• C15 kg
• D20 kg

Two gears, A and B, are in direct mesh. If Gear A rotates in a clockwise direction, which of the following describes the motion of Gear B?

• AIt rotates clockwise
• BIt rotates counter-clockwise
• CIt remains stationary
• DIt slides along its axle without rotating

A block and tackle pulley system has three supporting rope segments directly holding a load of 120 kg. Neglecting friction, what is the minimum effort force required to lift the load?

• A30 kg
• B40 kg
• C60 kg
• D120 kg

According to Pascal's Principle, if a force of 10 N is applied to a small piston with an area of 2 cm^2 in a closed hydraulic system, what is the resulting pressure transmitted throughout the fluid?

• A5 N/cm^2
• B10 N/cm^2
• C20 N/cm^2
• D50 N/cm^2

Gear A has 12 teeth and rotates at a speed of 100 revolutions per minute (RPM). It drives Gear B, which has 24 teeth. What is the rotational speed of Gear B?

• A50 RPM
• B100 RPM
• C200 RPM
• D240 RPM

Which of the following materials is the most efficient conductor of heat?

• AWood
• BGlass
• CCopper
• DAir

A heavy object is placed on a flat surface. In which of the following configurations will the object be the most stable against tipping over?

• ANarrow base and a high center of gravity
• BNarrow base and a low center of gravity
• CWide base and a high center of gravity
• DWide base and a low center of gravity

Water flows through a pipe that constricts to a narrower diameter in the middle section. According to Bernoulli's Principle, how do the speed and fluid pressure in the narrow section compare to the wider section?

• AHigher speed and higher pressure
• BHigher speed and lower pressure
• CLower speed and higher pressure
• DLower speed and lower pressure

Two identical light bulbs are connected to a battery. In Configuration A, they are connected in series. In Configuration B, they are connected in parallel. How does the brightness of the bulbs in Configuration A compare to Configuration B?

• ABulbs in A are brighter than B
• BBulbs in A are dimmer than B
• CBulbs in A and B have the same brightness
• DBulbs in A will flash, while bulbs in B remain steady

A simple pendulum swings back and forth. Which of the following changes will increase the time period (the time taken for one complete swing) of the pendulum?

• AIncreasing the mass of the bob
• BIncreasing the length of the string
• CDecreasing the mass of the bob
• DDecreasing the length of the string

A hydraulic jack has an input piston with an area of 5 cm^2 and an output piston with an area of 100 cm^2. If an input force of 50 N is applied to the small piston, what is the output force exerted by the large piston?

• A50 N
• B250 N
• C1000 N
• D2000 N

Two identical springs, each with a spring constant 'k' of 10 N/mm, are connected in series to support a load. What is the effective spring constant of the combined series system?

• A5 N/mm
• B10 N/mm
• C20 N/mm
• D40 N/mm

A siphon is used to drain water from an elevated tank to a lower container. What is the primary physical force that keeps the liquid flowing up and over the edge of the tank once the siphon is started?

• ACapillary action within the tube
• BAtmospheric pressure and gravity
• CCentrifugal force inside the bend
• DMagnetic fields within the liquid

A pair of scissors is an example of which class of lever?

• AFirst-class lever
• BSecond-class lever
• CThird-class lever
• DFourth-class lever

A wheelbarrow carries a load of 90 kg. The distance from the wheel axle (fulcrum) to the center of the load is 0.4 meters, and the distance from the axle to the handles (where effort is applied) is 1.2 meters. What effort force is required to lift the handles?

• A30 kg
• B45 kg
• C60 kg
• D90 kg

A belt drive connects two pulleys. The belt is crossed (twisted in an 'X' shape between the pulleys). If the driving pulley rotates clockwise, in which direction does the driven pulley rotate?

• AClockwise
• BCounter-clockwise
• CIt fluctuates direction continuously
• DIt will not rotate because a crossed belt locks the system

A solid block of wood floats in water with exactly half of its volume submerged. What can be inferred about the density of the wood block compared to the density of water?

• AThe wood is twice as dense as water
• BThe wood is half as dense as water
• CThe wood has the same density as water
• DDensity cannot be determined without knowing the mass of the block

A screw is used to hold two wooden blocks together. If the pitch of the screw thread is decreased (meaning the threads are closer together), how does this affect the effort required to turn the screw and the mechanical advantage?

• ARequires more effort, lower mechanical advantage
• BRequires less effort, higher mechanical advantage
• CRequires more effort, higher mechanical advantage
• DRequires less effort, lower mechanical advantage

A wooden crate rests on a ramp. The angle of the ramp is slowly increased. At an angle of 30 degrees, the crate just begins to slide down. What physical property determines this threshold?

• AThe coefficient of static friction
• BThe coefficient of kinetic friction
• CThe surface area of the crate in contact with the ramp
• DThe atmospheric pressure surrounding the ramp

A car drives around a circular track. If the car doubles its speed while keeping the same turning radius, how does the centrifugal force acting on the passengers change?

• AIt remains the same
• BIt doubles
• CIt triples
• DIt quadruples