Elective Mathematics Mock 2020

Question 1 of 50

Two fair coins are tossed. The probability of getting two heads is

Question 2 of 50

A force of 10 N acts on a 2 kg mass. Its acceleration is

Question 3 of 50

The momentum of a 3 kg body moving at 4 m/s is

Question 4 of 50

A binary operation * is defined by a * b = a + b + ab. Find 2 * 3.

Question 5 of 50

The number of terms in the expansion of (a + b)⁶ is

Question 6 of 50

Rationalise 1/√3.

Question 7 of 50

Evaluate log₁₀ 1000.

Question 8 of 50

The domain of f(x) = 1/(x − 2) excludes

Question 9 of 50

If A = [[1, 2], [3, 4]], find 2A.

Question 10 of 50

The order of a matrix with 2 rows and 3 columns is

Question 11 of 50

The distance between (1, 2) and (4, 6) is

Question 12 of 50

The midpoint of (2, 5) and (6, 1) is

Question 13 of 50

A line parallel to y = 3x − 2 has gradient

Question 14 of 50

The position vector of the point (−2, 5) is

Question 15 of 50

Convert 180° to radians.

Question 16 of 50

Find the exact value of sin 30°.

Question 17 of 50

Find the exact value of tan 45°.

Question 18 of 50

Differentiate y = 5x³ − 2x.

Question 19 of 50

The gradient of y = x² at x = 3 is

Question 20 of 50

The mean of 5, 7, 9, 11 is

Question 21 of 50

The standard deviation is the

Question 22 of 50

The class mark of the interval 10–19 is

Question 23 of 50

Two forces of 3 N and 4 N act at right angles. Their resultant is

Question 24 of 50

If a * b = 2a − b, find (3 * 1) * 2.

Question 25 of 50

Simplify √50 − √18.

Question 26 of 50

The nth term of the AP 3, 7, 11, ... is

Question 27 of 50

The 6th term of the GP 2, 6, 18, ... is

Question 28 of 50

If f(x) = 3x − 1, find f(f(1)).

Question 29 of 50

The transpose of [[1, 2], [3, 4]] is

Question 30 of 50

The line 2x + 3y = 6 cuts the y-axis at

Question 31 of 50

If p = 2i + 3j and q = i − j, find 2p − q.

Question 32 of 50

Two vectors a and b are perpendicular if

Question 33 of 50

In which quadrant are both sine and cosine negative?

Question 34 of 50

Evaluate lim (x→2) (x² − 4)/(x − 2).

Question 35 of 50

The interquartile range is

Question 36 of 50

A car accelerates from 10 m/s to 30 m/s over 200 m. Its acceleration is

Question 37 of 50

Solve 5^(x + 1) = 25^(x − 1).

Question 38 of 50

Express log 75 in terms of log 3 and log 5.

Question 39 of 50

Insert three arithmetic means between 4 and 20.

Question 40 of 50

Find the unit vector in the direction of a = 4i − 3j.

Question 41 of 50

Find the value of sin 240°.

Question 42 of 50

The coefficient of variation of data with mean 50 and SD 5 is

Question 43 of 50

A force F = (3i + 4j) N moves a particle from (1, 2) to (5, 6) m. The work done is

Question 44 of 50

A 5 kg mass is pulled up a smooth 30° incline by a force parallel to it. The force needed for constant velocity is (g = 10 m/s²)

Question 45 of 50

The function f(x) = x² − 4x on the domain x ≥ 2 is

Question 46 of 50

If A = [[1, 2], [3, 4]], find A².

Question 47 of 50

The acute angle between y = x and y = √3 x is

Question 48 of 50

Differentiate y = (3x − 1)/(x + 2).

Question 49 of 50

How many ways can a team of 5 be chosen from 6 boys and 4 girls if it must include exactly 2 girls?

Question 50 of 50

Use the binomial theorem to find (0.98)⁴ to 3 decimal places.