Practice the Mathematics Post UTME for Universities, Polytechnics and College of Education with our CBT software and pass your mathematics examination.

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MATHEMATICS POST UTME

MATHEMATICS POST UTME

MATHEMATICS POST UTME
BIOLOGY POST UTME/POST JAMB

Practice the Mathematics Post UTME for Universities, Polytechnics and College of Education with our CBT software and pass your mathematics examination.

1 / 40

Category: MATHEMATICS POST UTME

Which of the following is the formula for range?

L x H

L – H

H – L

H + L

Explanation:
H represents highest number in the data while L represents lowest number in the data, e.g 2,5,8,4,3,7; if you are asked to find range, range is 8 - 2 = 6.

2 / 40

Category: MATHEMATICS POST UTME

The lengths of the sides of a right-angled triangle are ym, (3y - 1)m and (3y + 1)m, find y.

12

9

8

4

3 / 40

Category: MATHEMATICS POST UTME

In an arithmetic sequence whose 4th term is 14 and whose 11th term is 70, the first term and common difference are

a =-14, d = 7

a = 10, d = 8

a = -10, d = 8

a = -7, d = 7

Explanation:
$a_{4} = a + 3 d = 14$ ..... (1)
$a_{11} = a + 10 d = 70$ ..... (2)
Solve simultaneously, subtract equation (1) from (2)
$7 d = 56$
$d = \frac{56}{7} = 8$
$a + 3 (8) = 14$
$a = 14 - 24 = - 10$

4 / 40

Category: MATHEMATICS POST UTME

The _______ is often the preferred measure of central tendency if the data are severely skewed.

Median

Mean

Range

Mode

5 / 40

Category: MATHEMATICS POST UTME

The sum of the first 20 terms of the progression 3, 6, 12, ... is

3(220 - 1)

3(220 + 1)

3(221 - 1)

3(221 + 1)

6 / 40

Category: MATHEMATICS POST UTME

Find the variance of the numbers k, k + 1, k + 2.

3

1

2/3

1/3

7 / 40

Category: MATHEMATICS POST UTME

Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2.

−34/27 , 73/27

1/3 , 2/5

2/3 , 4/5

27/34 , 34/27

8 / 40

Category: MATHEMATICS POST UTME

The most frequently occurring number in a set of values is called the ______.

Range

Mean

Median

Mode

9 / 40

Category: MATHEMATICS POST UTME

Find the principal which amounts to ₦4,400 at simple interest in 5 years at 2% per annum

₦3,800

₦5,200

₦5,000

₦4,000

Explanation:
Amount(A)=principal(P)+ simple interest(I)
Simple interest = PRT/100
A=P +PRT/100
Substitute the given values
4400= P + P×2×5/100
4400=P + P/10
Find the LCM
4400 =11P/10
Cross multiply
44000=11P
P = 44000/ 11
P= #4,000

10 / 40

Category: MATHEMATICS POST UTME

Tunse bought a house for ₦1,250,000.00 and spent ₦350,000.00 to renovate it. He then sold the house for ₦2,000,000.00. What is the percentage gain?

32%

65%

35%

40%

Explanation:
Tunde Bought A House For 1,250,000 And Renovate It For 350,000.
∴ The C.P is 1,250,000 + 350,000 = 1,600,000.
Gain = S.P - C.P = 2,000,000 - 1,600,000 = 400,000.
∴ To Calculate the Percentage (%) Gain = Gain / Cost Price * 100
i.e. 400,000 / 1,600,000 * 100 = 25%

11 / 40

Category: MATHEMATICS POST UTME

The heights in cm, of 10 children are 145, 163, 159, 162, 167, 149, 150, 160, 170, and 155. The standard deviation of the heights of the children is

5.7cm

7.7cm

6.5cm

5.5cm

12 / 40

Category: MATHEMATICS POST UTME

P is the point (2, 7) and Q is the point (6, 3). What is the gradient of PQ?

1

0.5

-0.5

-1

Gradient is denoted by m, which goes by the formula
$m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$
$m = \frac{(3 - 7)}{(6 - 2)}$
$m = \frac{- 4}{4}$
$m = - 1$

13 / 40

Category: MATHEMATICS POST UTME

Mr. Robson bought bags of orange for ₦2,500 each. He sold them for ₦90,000 at a loss of 20%. How many bags of orange did he buy?

60

50

80

45

14 / 40

Category: MATHEMATICS POST UTME

A ladder 20m long rests against a vertical wall so that the foot of the ladder 9m from the wall. The height (correct to 1 decimal place above the ground at which the upper end of the ladder touches the wall is

17.1m

17.9m

18.7m

18.1m

Explanation:
Using Pythagoras therom
Hyp²=adj² + opp²
According to the question 20m is the Hyp and the foot is the Adj which is 9m, I'm denoting the height as C
20²=9²+C²
400=81+C²
400-81=C²
C²= 319
C=√319
C= 17.8605
Approx to 1d.p
C=17.9

15 / 40

Category: MATHEMATICS POST UTME

One of these is not a desirable feature of a good statistical table

A table must reveal salient features of data

A table must be self sufficient

A table must be self explanatory

A table must clearly communicate information in a neat and concise form

16 / 40

Category: MATHEMATICS POST UTME

In an arithmetic sequence with 25 terms, if the first term is 60 and last term is -12 the common difference is

2

3

-2

-3

Explanation:
$L = a + [n - 1] d; L = - 12, a = 60, n = 25$
$- 12 = 60 + [25 - 1] d$
$- 12 = 60 + [24 d]$
$- 12 - 60 = 24 d$
$24 d = - 72$
$d = - \frac{72}{24}$
$d = - 3$

17 / 40

Category: MATHEMATICS POST UTME

Find the value of p, if the line which passes through (-1, p) and (-2p, 2) is parallel to the line 2y + 8x - 17 = 0.

-6/7

6/7

4/7

2/5

18 / 40

Category: MATHEMATICS POST UTME

If x and y are two real numbers such that 3x + 2y = 5 and 5x + 4y = 9, then 4x + 3y =

6

2

5

7

Explanation:
3x + 2y = 5 multiply by 4
5x + 4y = 9 multiply by 2
12x + 8y = 20
10x + 8y = 18 (eliminating y tru subtracting both equation)
2x = 2 so x = 1
Subs. x = 1 into
3(1) + 2y = 5
2y = 5 - 3, 2y = 2 so y = 1
x = 1, y = 1

19 / 40

Category: MATHEMATICS POST UTME

Statistics is a set of tools whose proper use will _______ the decision maker.

Completely fill the needs of

Aid

Confuse

Encumber

20 / 40

Category: MATHEMATICS POST UTME

A rectangular box with a square base and no top has a volume of 500 cm, the dimensions of the box that require the least amount of material are

50 × 5 × 2cm

25 × 10 × 2

10 × 10 × 5cm

4 × 5 × 25cm

21 / 40

Category: MATHEMATICS POST UTME

_________ are used when you want to visually examine the relationship between two quantitative variables.

Bar graphs

a Pie graphs

a Line graphs

a Scatterplots

22 / 40

Category: MATHEMATICS POST UTME

The ______ is the value you calculate when you want the arithmetic average.

Mean

Mode

All of the above

Median

23 / 40

Category: MATHEMATICS POST UTME

What is the length of an arc of a circle with a radius of 5 if it subtends an angle of 60° at the center?

10.48

5.24

3.14

2.62

Explanation:
Length of an arc formula
L = Circumference $\times$ fraction of circle
L = $2 π R \times \frac{θ}{360}$
L = $2 \times \frac{22}{7} \times 5 \times \frac{60}{360}$
L = 5.238

24 / 40

Category: MATHEMATICS POST UTME

The chances of three independent events P, Q, R occurring are $\frac{1}{2}$ , $\frac{2}{3}$ , $\frac{1}{4}$ respectively. What are the chances of P and Q only occurring?

2/9

2/3

1/2

1/4

25 / 40

Category: MATHEMATICS POST UTME

Which of the following points does not lie on the line 2y + 5x -4 = 0?

(1,-0.5)

(0, 2)

(2, 3)

(0.8, 0)

26 / 40

Category: MATHEMATICS POST UTME

Find the point on the Euclidean plane where the curve y = 2x² - 2x + 9 has 2 as gradient.

(1, 4)

(3, 5)

(1, 3)

(2, 4)

27 / 40

Category: MATHEMATICS POST UTME

The second and fifth terms of a geometric progression a 21 and 567 respectively. Find the first time and the common ratio of the progression.

-3, 7

3, 7

-7, 3

7, 3

Explanation:
2nd term $= a r = 21$ , 5th term $= a r^{4} = 567$
$\Rightarrow \frac{5th term}{2nd term} = \frac{a r^{4}}{a r}$
$= \frac{567}{21} = 27$
$r^{3} = 27$
$r = 3$
$a r = 21$
$a (3) = 21$
$\Rightarrow a = 7$
Ans: $7, 3$

28 / 40

Category: MATHEMATICS POST UTME

The length of a rectangle is three times its width. If the perimeter is 72 cm, the width of the rectangle is

9cm

10cm

6cm

8cm

Explanation:
From The Question. L = 3 Times Width
L = 3w
P = 72
W = ?
From The 4mula, P = 2l + 2w
but l = w
Therefore, P = 2(3)w + 2w
72 = 6w + 2w
72 = 8w
w = $\frac{72}{8}$
w = 9cm

29 / 40

Category: MATHEMATICS POST UTME

A housewife bought five yams at Y34 per yam and three oranges at Y5 each where Y is the currency reckoned in base six. The total amount spent by the housewife is

Y2526

Y3156

Y2256

Y3526

30 / 40

Category: MATHEMATICS POST UTME

Rationalize $\frac{(4 \sqrt{7} + \sqrt{2})}{(\sqrt{2} - 7)}$

√14 - 8

-√14 - 6

3√14 - 28

2√14 - 6

31 / 40

Category: MATHEMATICS POST UTME

A straight line has a gradient of -2 and passes through the point (4, 1). What is its equation?

y + 2x = 6

2y = x -2

y = 2x - 6

y + 2x – 9 = 0

$y = m x + c$ at point $(4, 1)$
$1 = - 2 (4) + c$
$c = 1 + 8$
$c = 9$
Into original equation:
$y = - 2 x + 9$
$y + 2 x - 9 = 0$

32 / 40

Category: MATHEMATICS POST UTME

In an arithmetic sequence with 25 terms, if the first term is 60 and last term is -12, the sum of the terms of the sequence is

2400

900

600

1800

Explanation:
$- 12 = 60 + (25 - 1) d$
$24 d = - 72$
$d = - 3$
$s = \frac{n}{2} (2 a + (n - 1) d)$
$\frac{25}{2} (2 \times 60 + (25 - 1) - 3)$
$\frac{25}{2} (120 - 72)$
$\frac{25}{2} (48)$
$= 600$

33 / 40

Category: MATHEMATICS POST UTME

Ann goes swimming regularly. She wants to improve her fitness, so she decides to swim 10 lengths in the first session and increase the number of lengths she swims by 2 every session. When she reaches 50 lengths in a session she will not increase the number any further. Ann decides she will give herself a reward
when she has swum a total of 400 lengths. After how many sessions does she get her reward?

16

25

15

24

Sn=400
n=?
d=2
Sn= n/2(2a+(n-1)d
400=n/2(2*10+(n-1)2
400=n/2(20+2n-2)
400=n/2(18+2n)(cross multiply)
400*2=n(18+2n)
800= 18n+2n^2
Divide both sides by 2
Then we have;
400=9n+n^2
n^2+9n-400=0
Using quadratic formula;
Y=-b+-√b^2-4ac/2a
n^2+9n-400=0
ax^2 +bx+c=0
a=1, b=9 c=-400
Y=-9+-√9^2-4*1*-400/2*1
Y=-9+-√8+1600/2
Y=-9+-√1608/2
Y=-9+-40.0/2
Y=-9+40/2 or -9-40/2
Y=15.5 or -24.5
Y~16 or -25

34 / 40

Category: MATHEMATICS POST UTME

At what value of x is the function y = x² - 6x - 7 minimum?

6

3

2

5

35 / 40

Category: MATHEMATICS POST UTME

In a class, 120 students speak English or French or both. 70 speak English and 55 speak French. How many speak English but not French?

60

50

45

65

36 / 40

Category: MATHEMATICS POST UTME

List the integral values of which satisfy the inequality $- 2 < 7 - 3 x \leq 10$ .

0, 1, 2

1, 2, 3

-1, 0, 1, 2

-2, 0, 1

37 / 40

Category: MATHEMATICS POST UTME

What is the slope of the line that is perpendicular to y - 2x = 1?

1/2

-1/2

-2

2

38 / 40

Category: MATHEMATICS POST UTME

A is the point (1, 5), B is the point (4, 7) and C is the point (5, 2). Triangle ABC is

Equilateral

Right-angle

Scalene with no right angle

Isosceles

Explanation:
A scalene triangle has no side equal so if you check points ABC you will notice that no side is equal.

39 / 40

Category: MATHEMATICS POST UTME

If x = 2, then (x - 1)(2x - 3) =

3

0

-1

1

Explanation:
Since x = 2,
=> {2-1}{2(2)-3}
={1}{1} = 1

40 / 40

Category: MATHEMATICS POST UTME

A frustum of a pyramid is 3cm square at the top and 6cm square at the bottom and is 5cm high. The volume in cm³ of the frustum is

15

115

150

105

Your score is

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