Expand and simplify (2x - 3)(x + 5).
Mathematics
Question · Medium
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Short
Solve for x: 3(x - 2) = 2x + 7.
Simplify the surd expression sqrt(50) + sqrt(8).
Question · Easy
Evaluate 27^(2/3) without a calculator.
A line has equation 2y = 6x - 4. What is its gradient?
Cruise the loop: a log is an exponent
Differentiate y = 4x^3 - 5x + 7 with respect to x.
Find the value of the integral of (6x + 2) dx evaluated from x = 0 to x = 2.
The quadratic x^2 - 6x + 8 = 0 has roots. What is the sum of its roots?
Solve log_2(x) = 5.
The carpenter's square-corner trick
Without a calculator, what is the exact value of sin(30 degrees) + cos(60 degrees)?
An arithmetic sequence has first term 5 and common difference 3. What is the 10th term?
A fair six-sided die is rolled twice. What is the probability that both rolls show a 6?
The function f(x) = x^2 - 4x + 3 is written in completed-square form a(x - h)^2 + k. What is the minimum value of f(x)?
Question · Hard
The houseplant does both
Find the equation of the tangent to y = x^2 at the point (3, 9).
A circle has equation (x - 1)^2 + (y + 2)^2 = 25. What is the radius?
Simplify (x^2 - 9) / (x + 3) for x not equal to -3.
The first three terms of a geometric sequence are 4, 12, 36. What is the sum of the first five terms?
Same battery. Which lets more through?
Solve the simultaneous equations 2x + y = 7 and x - y = 2.
What is the coefficient of x^2 in the binomial expansion of (1 + x)^5?
A right-angled triangle has legs of length 5 and 12. What is the length of the hypotenuse?
Solve the inequality 2x - 3 > 5.
Find x
The points A(1, 2) and B(4, 6) are given. What is the distance AB?
Find the x-coordinate of the stationary point of y = x^2 - 8x + 1.
Express 0.000045 in standard form.
A bag contains 3 red and 5 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
Factor it
Solve 2x^2 - 5x - 3 = 0.
Without a calculator, evaluate (3/4) divided by (2/3).
The graph of y = f(x) is transformed to y = f(x - 2) + 3. Describe the transformation.
Given log(2) is approximately 0.301, what is log(8) to 3 decimal places? (log is base 10.)
A sector of a circle has radius 6 cm and angle 60 degrees. What is its area? (Use pi.)
If f(x) = 3x + 1 and g(x) = x^2, what is f(g(2))?
The discriminant of kx^2 + 4x + 1 = 0 is zero for repeated roots. What is the value of k?
Evaluate the limit-free derivative: differentiate y = (2x + 1)^3 with respect to x using the chain rule.
What is the area enclosed between the curve y = x^2 and the x-axis from x = 0 to x = 3?
A and B are events with P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.2. Are A and B independent?
Solve 5^(x) = 125.
The mean of five numbers is 12. Four of them are 10, 11, 13, and 15. What is the fifth number?
Rationalise the denominator of 6 / sqrt(3).
A curve has dy/dx = 6x - 4 and passes through (1, 5). Find y in terms of x.
In a triangle, two angles are 35 degrees and 65 degrees. Using the sine rule context, what is the third angle?
A car accelerates uniformly from rest to 20 m/s in 8 s. What is its acceleration?
Physics
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