2022 - JAMB Mathematics Past Questions and Answers - page 4
In the diagram shown, XY = 8cm and OX = 5cm. Find Oz
9cm
3.4cm
9.1cm
3cm
hyp = 5cm, adj = \(\frac{8cm}{2}\) 4cm, opp = xcm
Appy Pythagoras' theorem:
hyp\(^2\) = opp\(^2\) + adj\(^2\)
5\(^2\) = x\(^2\) + 4\(^2\)
x\(^2\) = 25 - 16
x = √9
x = 3cm
Let (*) be a binary operation on a natural number defined by a * b = a - b + (ab)\(^2\), then find 3 * 5
223
232
32
-232
3 * 5 = 3 - 5 + (3 x 5)\(^2\)
-2 + (15)\(^2\)
-2 + 225
= 223
If y varies inversely as x and x = 3 when y =4. Find the value of x when y = 12.
4
1
2
3
Given that y is inversely proportional to x,
y = 1/x; y = \(\frac{k}{x}\)
k =xy → 3 * 4 = 12
x = \(\frac{k}{y}\)
x = \(\frac{12}{12}\) = 1
If 8, p, q and 26 is an A.P. Find the values of p and q.
p = 14 and q = 14
p = 20 and q = 14
p = 20 and q = 20
p = 14 and q = 20
Common difference = 6
Hence, add 6 to get the next terms:
8, 14, 20 and 26
Find x if the mean of 2x, 4x, 2x - 13 and 6x is 4.
1.5
2.0
1.0
0.5
Mean (4) = \(\frac{2x + 4x + 2x - 13 + 6x}{4}\)
16 = 14x - 13
16 + 13 = 14x
x = 29/14 or 2.07
Factorize 4a\(^2\) - 9b\(^2\)
(2a-3b) (2a+3b)
(2a-b) (2a+3b)
(2a-3b) (a+3b)
(a-3b) (a+3b)
Trial:
(2a-3b) (2a+3b)
4a\(^2\) + 6ab - 6ab - 9b\(^2\)
4a\(^2\) - 9b\(^2\)
If n(P) = 20 and n(Q) = 30 and n(PuQ) = 40, find the value n(PnQ).
10
30
15
40
n(PuQ) = n(p) + n(q) - n(PnQ)
40 = 20 + 30 - n(PnQ)
n(PnQ) = 50 - 40 = 10
Three times a certain number (x), minus 2 is less than the number minus 6. Find the possible values of x.
x <-2
x>2
x>-2
x<2
- three times a certain number (x) => 3x
- minus 2 = -2
- is less than = <
- the number minus 6 = x -6
Hence; 3x - 2 < x - 6
3x - x < -6 + 2
2x < -4
x < -2 is the possible value of x
The number line is represented by inequality.
x≤2
x<2
x≥2
x>2
The arrow points in the direction of all numbers greater than 2
Hence,
x ≥ 2
If a dress is sold for #3800.00 at a 20% discount. what is its original price?
#3,000.00
#4,000.00
#5,000.00
#4,750.00
Given that the cost of the dress reduces to #3800.00 by the discount,
Assume the original price = x
x – (20% of x) = 100
x – 0.2x = 100
0.8x = #3800
x = \(\frac{3800}{0.8}\)
x = 4,750