A function is defined by f(x) = 3x - 5. What is the value of f(4)?
Functions
Question · Easy
Would you rather: marbles
Short
Given f(x) = 2x + 1 and g(x) = x^2, find the composite function gf(x).
Question · Medium
The function f(x) = 4x - 3 has an inverse f^-1(x). What is f^-1(x)?
The quadratic equation x^2 - 6x + 8 = 0 has roots p and q. What is the value of p + q?
Quadratic Equations
For the quadratic equation 2x^2 + 3x + k = 0 to have two equal roots, what is the value of k?
Cruise the loop: a log is an exponent
The quadratic function f(x) = (x - 3)^2 + 4 is expressed in vertex form. What are the coordinates of its minimum point?
Quadratic Functions
The quadratic function f(x) = x^2 + 2x + 5 does not intersect the x-axis. This is because its discriminant is which of the following?
Solve the simultaneous equations x + y = 5 and x^2 + y^2 = 13. Which pair is a valid solution?
Systems Of Equations
Simplify 3 log_a 2 + log_a 5 as a single logarithm.
Indices Surds And Logarithms
Factor it
Solve the equation 2^(x+1) = 16.
Simplify the surd expression (sqrt 12) + (sqrt 27).
An arithmetic progression has first term a = 3 and common difference d = 4. What is the 10th term?
Progressions
A geometric progression has first term 2 and common ratio 3. What is the sum of the first 4 terms?
A geometric progression has first term 8 and common ratio 1/2. What is the sum to infinity?
A set of data y and x is related by y = ax^2 + b. To reduce this to linear form Y = mX + c by plotting a straight-line graph, which variables should be plotted on the axes?
Linear Law
The points A(1, 2) and B(7, 10) are given. What is the midpoint of the line segment AB?
Coordinate Geometry
What is the equation of the straight line with gradient 2 passing through the point (1, 3)?
Two lines have gradients m1 = 3 and m2. If the lines are perpendicular, what is the value of m2?
Given vectors a = 3i + 4j, what is the magnitude |a|?
Vectors
Given vectors a = 2i + 3j and b = 4i - j, find a + b.
In triangle ABC, a = 8 cm, b = 6 cm and the angle C = 60 degrees. Using the cosine rule, what is the length of side c?
Solution Of Triangles
In triangle PQR, angle P = 40 degrees, angle Q = 60 degrees and side p = 10 cm. Using the sine rule, which expression gives side q?
A triangle has two sides of length 7 cm and 9 cm with an included angle of 30 degrees. What is the area of the triangle?
In a base year, the price of an item is RM50 and in the current year it is RM65. What is the price index of the item for the current year based on the base year?
Index Numbers
The price indices of three components A, B and C are 120, 110 and 130, with weights 2, 3 and 5 respectively. What is the composite (weighted) index?
Question · Hard
Convert the angle 1.5 radians to degrees. (Use pi = 3.142.)
Circular Measure
A circle has radius 6 cm. An arc subtends an angle of 1.2 radians at the centre. What is the length of the arc?
A sector of a circle has radius 10 cm and a central angle of 0.8 radians. What is the area of the sector?
Differentiate y = 3x^4 with respect to x.
Differentiation
Given y = (2x + 1)^5, find dy/dx using the chain rule.
The curve y = x^2 - 4x + 7 has a turning point. At what x-value does it occur?
For the curve y = x^2 - 4x + 7, the second derivative is d^2y/dx^2 = 2. What does this tell you about the turning point at x = 2?
The radius of a circle increases at a rate of 0.2 cm per second. When the radius is 5 cm, what is the rate of increase of the area? (Area A = pi r^2, use the chain rule dA/dt = dA/dr times dr/dt.)
Integrate the function 6x^2 with respect to x.
Integration
Evaluate the definite integral of 2x with respect to x from x = 1 to x = 3.
The area bounded by the curve y = x^2, the x-axis and the lines x = 0 and x = 2 is found by integration. What is this area?
Given that dy/dx = 4x + 1 and the curve passes through the point (1, 5), what is the equation of y?
How many different 3-letter arrangements (permutations) can be formed from the letters of the word 'CAT', using each letter once?
Permutations And Combinations
In how many ways can a committee of 3 people be chosen from a group of 7 people?
How many distinct arrangements can be made using all the letters of the word 'LEVEL'?
A fair die is rolled once. What is the probability of getting a number greater than 4?
Probability Distribution
A binomial experiment has n = 5 trials with probability of success p = 0.4. What is the mean (expected number of successes)?
For a binomial distribution with n = 5 and p = 0.4, what is the variance?
A continuous random variable X follows a normal distribution with mean 50 and standard deviation 10. What is the standardised value (z-score) of X = 65?
Given that sin theta = 3/5 and theta is acute, what is the value of cos theta?
Trigonometric Functions
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