Express 25_ten as a number in base two.

Find the value of a³ + 2ab² + b³,

when a = 2 and b = – 1

Use the addition and multiplication tables for modulo 5 shown below to answer the following:

Find the truth set of

(n ⊗ 4) ⊕ (n ⊗ 4) = 1(mod 5)

Use the addition and multiplication tables for modulo 5 shown below to answer the following:

What is the truth set of n 0 n = 4(mod5)

Consider the following statement:

If one works hard one must pass his or her examination.

Which of the following is a valid conclusion from the statement?

The following table shows the mapping

x →y . What is the rule for the mapping?

X 0 2  4  6  8
↓ ↓  ↓  ↓  ↓  ↓
y 5  3 1 -1 -3

In the right angle triangle POR shown

below, sin Ȓ equals

Express 75882 to three significant figures.

Find the vector which translates the point (2, 4) to the point (5, 3).

P is equidistant from Q and R. The bearing of Q from P is 70° and the bearing of R from P is 130°. What is the bearing of R from Q?

If x is a positive real number, which of the following implication is/are true?

I.      1/x  > 1/3 ⇔ x > 3

II.      x² > 16 ⇔ x < 5

III.  5 – x < 0  ⇔  x > 5

Evaluate without using tables:

√147 – √75 + √27

If log3 3 = a and log10 5 = b, find in terms of a and b, the value of log10 75.

In a class of 40 students, 30 of them read Chemistry and 20 read Physics. What is the probability that a student chosen at random in the class read both Chemistry and Physics?

Evaluate 3√(3⁶ x 5³)  

Leaving your answer in the prime factors.

The histogram below shows the marks distribution of a class of 15 pupils. Use it to answer the following:

Calculate the mean mark of the class.

The histogram below shows the marks distribution of a class of 15 pupils. Use it to answer the following:

Find the median mark for the class.

Multiply 6.4 x 10^-2 by 8.5 x l0⁴ and leave your answer in standard form.

Make h the subject of the relation

V=1/3πr²h

When the point (3, 4) is reflected in line I its image is (-4, -3). What is the equation of I?

In the diagram below, find the sum of x and y.

Water flows from a tap into an empty cylindrical jar at the rate of 32π cm³ ç second. If the radius of the jar is 4cm, find the height of the water in the jar after two seconds.

A trader gives 5% discount for cash payment. What discount will be allowed on a bill of ¢56,000.00 for cash payment?

In the diagram, O is the centre of a circle of radius 5cm. If the angle POS is 60^o, what is the area of the shaded sector?

If E= {a, b, c, d, e}, P = {a, b, c} and Q = {a, b}. Which of the following statement is/are true?

P, Q and R are sets such that P ⊂ Q and Q ⊂ R. Which of the following is/are correct illustrations of the given information?

P, Q and R are subsets of {2, 3, 4, 5, 6, 7, 8, 9). If P={x: x < 6}, Q={y: 3 < y < 8} and R = {even numbers}. Find P ∩ Q ∩ R

The points P(2, 4) is rotated about the origin in the co-ordinate plane through a clock-wise angle 270°. Find the image P¹

PQ = (2) (4)

RQ = (-1) (5)

Find PR

PQ, RS, TU, and GH are straight lines

PQ//RS//TU. What kind of angles are V and W?

PQR, SQT, MQN are straight lines.

LPQS = 25° and ZMQT = 85°. Find the value of x.

A function g is defined by g:x (2x-1)/x. For what value of x is g undefined?

What is the size of angle PQT in the construction?

Arrange 123 four, 42 six, 28 ten in descending order of magnitude.

A quantity z varies directly as x and inversely as cube of y. If z = 2, x = 2 and y = 1. Find the relation of z in terms of x and y.

Which of the following is/are rational?

I. P={2, √3, 5}

II. Q={7, 1/6, √9}

III. R={-3 ≤ x ≤ 8}

Find the value of (t — s) from the relations:

4s – t + 1=0 and 2t – 5s+1=0

If 2/a = 1/b – 1/d.

Find an expression for d in terms of a and b.

Factorise completely the expression

(h² – k²) – p(h – k).

U = {Triangles},

S = {Isosceles triangles),

Q = {Equilateral triangles} and

R = {Right angle triangles).

Which of the Venn diagrams is the correct illustration?

The graph shows the function f(x) = x² – 3x, for the interval -2.5 ≤ x ≤ 5.5. Use it to answer the following:

What is the equation of the axis of symmetry?

The graph shows the function f(x) = x² – 3x, for the interval -2.5 ≤ x ≤ 5.5. Use it to answer the following:

Find the truth set of x²—3x = 10.

The graph shows the function f(x) = x² – 3x, for the interval -2.5 ≤ x ≤ 5.5. Use it to answer the following:

For what values of x is y < 0

In the diagram, PQRS is a circle with centre O. |QR| = |RS| and ∠QOR = 70°. Find the value of x.

Find the truth set of the inequality

2t + 5 < 4t – 5

Which of the following illustrates the solution set of {x: 1 ≤ 3x—5 ≤ 7}.

Find the truth set of (x—2) (x+ 3)=0

If P = {2, 4, 6, 8, 10), which of the following adequately defines P.

The diagonal of a rhombus are 8 cm and 6 cm. Calculate the length of the side of the rhombus.

Which of the following statements is false?