Core Mathematics — 2020

Evaluate and correct to two decimal places: 75.0785 − 34.624 + 9.83.

If X = {x : x < 7} and Y = {y : y is a factor of 24} are subsets of μ = {1, 2, 3 . . . 10}, find X ∩ Y .

Simplify [( 16 9 )− 3 2 × 16− 3 4 ] 1 3 .

Express 1 + 2log103 in the form of log10x.

If 101two + 21y = 33five , find the value of y.

An amount of N 550, 000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x.

Given that √3+√5 √5 = x + y√15, find the value of (x + y).

If x = 3 and y = −1, evaluate 2(x2 − y3).

Solve 3x − 2y = 10 and x + 3y = 7 simultaneously.

The implication x → y is equivalent to?

The first term of a geometric progression is 3 and the 5th term is 48. Find the common ratio.

Solve 1 3 (5 − 3x) < 2 5 (3 − 7x).

Make m the subject of the relation k = √ m−y m+1 .

Find the quadratic equation whose roots are 1 2 and − 1 3 .

Given that x is directly proportional to y and inversely proportional to z, x = 15 when y = 10 and z = 4, find the equation connecting x, y and z.

Two buses start from the same station at 9.00 am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240 km apart?

A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area.

In the diagram, P Q||SR. Find the value of x.

Find the equation of the line parallel to 2y = 3(x − 2) and passes through the point (2, 3).

The expression 5x+3 6x(x+1) will be undefined when x equals:.

A man is five times as old as his son. In four years’ time, the product of their ages would be 340. If the son’s age is y, express the product of their ages in terms of y.

Simplify a b − b a − c b .

In the diagram, XY Z is an equilateral triangle of side 6 cm and Y is the midpoint of XY . Find tan(∠XZT ).

A fence 2.4 m tall, is 10 m away from a tree of height 16 m. Calculate the angle of elevation of the top of the tree from the top of the fence.

Fati buys milk at $x per tin sells each at a profit of $y. If she sells 10 tins of milk, how much does she receives from the sales?

If tan y is positive and sin y is negative, in which quadrant would y lie?

The dimension of a rectangular base of a right pyramid is 9 cm by 5 cm. If the volume of the pyramid is 105 cm3, how high is the pyramid?

Each interior angle of a regular polygon is 168◦. Find the number of sides of the polygon.

In the diagram, M N ||P Q, ∠MNP = 2x, and ∠NPQ = (3x − 50)◦. Find the value of ∠NPQ.

The length of an arc of a circle of radius 3.5 cm is 1 19 36 cm. Calculate, correct to the nearest degree, the angle substended by the centre of the circle. [Take π = 22 7 ]

In the diagram, P U ||SR, P S||T R, QS||U R, |U R| = 15 cm, |SR| = 8 cm, |P S| = 10 cm and the area of the triangle SU R is 24 cm2. Calculate the area of P T RS.

In the diagram, there is a circle with center O. If ∠OP Q = 48◦, find the value of m.

The pie chart shows the population of men, women, and children in a city. If the population of the city is 1, 800, 000, how many men are in the city?

The mean of the numbers 15, 21, 17, 26, 18 and 29 is 21. Calculate the standard deviation.

Find the sum of the interior angle of a pentagon.

The diameter of a sphere is 12cm. Calculate, correct of the nearest cm3, the volume of the sphere. [Take π = 22 7 ]

A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If a ball is selected at random from the box, what is the probability that it is green?

A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If two balls are selected at random one after the other with replacement, what is the probability that both are red?

In the diagram, P Q is a straight line. If m = 1 2 (x + y + z), find value of m.

x 6.20 6.85 7.50 y 3.90 5.20 6.50 The points on a linear graph are as shown in the table. Find the gra- dient (slope) of the line.

In the diagram below, O is the center of the circle. P Q and RS are tangents to the circle. Find the value of (m + n)◦.

Which of the following is not a sufficient condition for two triangles to be congruent?

A woman received a discount of 20% on a piece of cloth she purchased from a shop. If she paid $525.00, what was the original price?

The interquartile range of distribution is 7. If the 25th percentile is 16, find the upper quartile.

The graph of the equations y = 2x + 5 and y = 2x2 + x − 1 are shown. Use the information above to find the points of intersection of the two graphs.

The graph of the equations y = 2x + 5 and y = 2x2 + x − 1 are shown. Use the information above to answer this question. If x = −2.5, what is the value of y on the curve?

If (x + 2) is a factor of x2 + px − 10, find the value of p.

In the diagram, O is the centre of the circle. If ∠N LM = 74◦, ∠LM N = 39◦ and ∠LOM = x, find the value of x.

Find the least value of x which satisfies the equation 4x = 7(mod9).