Focus SPM 2022 - Mathematics

Mathematics SPM  Answers 

ANSWERS

Form 4 (e) f(x) (f) f(x)
x
1Chapter Quadratic Functions and Equations in
One Variable 0
–4 4

Penerbitan Pelangi Sdn Bhd. All Rights ReservedTry This! 1.1 x
–2 0

1. (a) Yes, the expression only has one variable, x, and the 14. x = 7
highest power of x is 2.
15. 2 hours
(b) Yes, the expression only has one variable, u, and the 16. The product of two consecutive odd numbers is 323. x = 17
highest power of u is 2.
17. RM24
(c) No, because the highest power of variable x is 1.
(d) No, because the highest power of variable x is 3. 18. (a) No
(e) Yes, the expression only has one variable, x, and the (b) Yes
(c) No
highest power of x is 2.
(f) No, because the highest power of variable x is 1.

2. (a) Parabolic shape opens up with a minimum point. SPM Practice 1
(b) Parabolic shape opens up with a minimum point.
(c) Parabolic shape opens down with a maximum point. PAPER 1
(d) Parabolic shape opens down with a maximum point.
1. C
3. (a) The shape of the graph is and the width decreased. 6. C 2. A 3. D 4. B 5. A
(b) The shape of the graph is and is on the right of the 7. B 8. D 9. C 10. A
y-axis.
and moves vertically PAPER 2
(c) The shape of the graph is
downwards.

4. The graph moves 12 units vertically upwards. 1. x = 2, –9

5. f(x) = 2x2 + 16x 2. x = 3 ,  –2
5
6. f(x) = 12x2 + 31x + 9
3. 30
7. (a) f(x) = 10x2 – 33x – 28 (b) 10x2 – 33x – 86 = 0

8. (a) f(x) = 7x2 + 26x – 6 (b) 7x2 + 26x – 126 = 0 4. 0.2 m
5. P(–1, 0) and Q(4, 0)
9. (a) No  (b) Yes (c) Yes (d) No

10. (a) Yes    (b) No (c) Yes (d) No 6. f(x)

11. (a) 0, 8 (b) 0, –  25 (c) 0, 3  
(d) –6, 6 (e) –  52 ,  25 2
x
(f)  –   3 ,  32 –8 0 2
2

12. (a) –3, –5 (b) 3, –8 (c) 4, –  72

(d) 5 , –   2 (e) 6, 2 (f)  –   9 , 3 –8
2 3 3 2 2

13. (a) f(x) (b) f(x)

10 12

02 5 x 7. f(x) = –  74 x2 – 28x + 112
(c) f(x) 8. x = 4
–3 0 x
4 9. 304 m2
10. Bus A is 90 km and bus B is 120 km away from the bus station.
(d) f(x)
11. 6 seconds
3 12. x = 60, h = 45

– –13 0 x –1 0 –43 x 13. They have to sell 32 slices of cheese cake with the price of
–2 2 RM5 per slice or sell 40 slices of cheese cake with the price
of RM4 per slice.

14. The measurement of the photo is 15 cm × 12 cm

335

  Mathematics SPM  Answers

2Chapter SPM Practice 2

Number Bases

Try This! 2.1 PAPER 1 2. B 3. B 4. D 5. C
7. B 8. A 9. D 10. A
1. (a) 23 1. B 12. C 13. D 14. B 15. D
(b) 41 6. C 17. B 18. C 19. C 20. A
(c) 72 11. D
(d) 60 16. D

Penerbitan Pelangi Sdn Bhd. All Rights Reserved 2. (a) 500PAPER 2
(b) 16
(c) 7 1. (a) 54
(d) 12 (b) 5
(c) 15
3. (a) 55 (d) 144
(b) 95
(c) 34 2. (a) 2123
(d) 89 (b) 211203

4. (a) 100012 3. (a) 2107
(b) 1001111102 (b) 657
(c) 10011002
4. (a) 293
5. (a) 2015 (b) 51
(b) 21135 (c) 63
(c) 1005 (d) 44

6. (a) 326 5. 2100336
(b) 1336
(c) 55156 6. (a) 2
(b) 2223
7. (a) 458
(b) 658 7. (a) P = 333, Q = 135
(c) 1608 (b) R = 235, 245, 305, 315

8. (a) 2358 8. (a) X = 145, 205, 215
(b) 7348 (b) 2
(c) 11011102
(d) 111001112 9. (a) 1100012
(b) 549
9. (a) 1204
(b) 4225 10. (a) 7
(c) 14246 (b) 1
(d) 10001012
(e) 268 11. (a) 5
(f) 2619 (b) 3

10. (a) 110203 12. (a) 3
(b) 40205 (b) 1
(c) 2006
(d) 278 13. (a) 2425
(b) 3345
11. (a) 2126
(b) 889 14. (a) 457
(b) 517
12. Y = 1215, 1225, 1235, 1245

336

Mathematics SPM  Answers 

3Chapter Logical Reasoning (c) Rhombus is a square or a parallelogram.
(d) 52 – 32 = 42 or 82 – 72 = 52
(e) Point (0, 4) or point (4, 0) lies on y-axis.

Try This! 3.1 9. (a) True (b) True
(c) False (d) False
(e) False
1. (a) Statement. A true statement.
(b) Not a statement. Cannot determine whether the sentence 10. ~p ~q p q pq
is true or false. (a) 3 77 3
(c) Not a statement. Cannot determine whether the sentence (b) 3 37 7
is true or false. (c) 7 73 3
(d) Not a statement. Cannot determine whether the sentence (d) 3 77 3
is true or false.
(e) Statement. A true statement.
(f) Statement. A false statement.
(g) Not a statement. Cannot determine whether the sentence
is true or false.
(h) Not a statement. Cannot determine whether the sentence
is true or false.
Penerbitan Pelangi Sdn Bhd. All Rights Reserved 11. (a) If m = 1 , then m3­ = 1 .
2 8
(b) If PQR is a right-angle triangle, then sides PQ, QR and PR

2. (a) False (b) True satisfy Pythagoras’ theorem.
(c) False (d) True a
(e) True (f) False (c) If b , 0, then a , 0 or b , 0.
(g) True (h) True
(d) If p . q, then p – q . 0.

3. (a) True: 16 + 23  32 12. (a) Antecedent : The side of the square is a cm.
False: 16  23 + 32 Consequent : The area is a2 cm2.

(b) True: 2 × 3 ÷1=1 (b) Antecedent : n(X) = 0
3 2 Consequent : X = {  }

False: 2 ÷ 3 ×1=1 (c) Antecedent : pq = 0
3 2 Consequent : p = 0 or q = 0

(c) True: 9 × 3 ≠ 4 × 2

False: 9 × 4 ≠ 3 × 2 (d) Antecedent : A(x1 , y1) and B(x2 , y2) y2 – y1
(d) True: {2, 4} , {2, 3, 4} x2 – x1
False: {2, 3, 4} , {2, 4} Consequent : The gradient of AB =

4. (a) Some (b) All 13. (a) mn = –1 if and only if m = – 1 .
(c) All (d) All n
(b) a is the factor of b if and only if b is the multiple of a.
(e) Some
(c) 3√x  = –1 if and only if x = –1.
5. (a) z3 – 5 is not a linear expression. (true)
(b) x + 3 does not exceed x by 3. (false) 14. (a) If p2 is an even number, then p is an even number.
(c) { }  {a, b} (false) If p is an even number, then p2 is an even number.
(d) 0.012 ≠ 1 × 10–2 (true)
(b) If θ is an obtuse angle, then 90°  θ  180°.
6. (a) ~p : Not all multiples of 4 are multiples of 10
p : False If 90°  θ  180°, then θ is an obtuse angle.
~p : True
(b) ~p : √0.004 ≠ 0.02 (c) If x3x.is3a, nthiemnpr3xopiesr fraction, then x . 3.
p : False If an improper fraction.
~p : True
(c) ~p : Cylinder does not have a curve surface. (d) If h is a positive number, then h . 0.
p : True If h . 0, then h is a positive number.
~p : False
15. (a) Converse: If 4 is the factor of 16, then 16 is the multiple
7. (a) Trapezium is a parallelogram. (false) of 4.
Trapezium is a rectangle. (false)
Trapezium is a parallelogram and a rectangle. (false) Inverse: If 16 is not the multiple of 4, then 4 is not the
(b) All prime numbers are odd numbers. (false) factor of 16.
All prime numbers are numbers which cannot be divided by
other numbers except 1 and itself. (true) Contrapositive: If 4 is not the factor of 16, then 16 is not
All prime numbers are odd numbers or numbers which the multiple of 4.
cannot be divided by other numbers except 1 and itself.
(true) (b) Converse: If x . y, then x – y . 0.
(c) Triangle is a three-dimensional shape. (false) Inverse: If x – y < 0, then x < y.
Pyramid is a three-dimensional shape. (true)
Triangle or pyramid is a three-dimensional shape. (true) Contrapositive: If x < y, then x – y < 0.
(d) a × 1 = a (true) (c) Converse: If a . 0, then y = ax2 + bx + c has a minimum
a ÷ 1 = a (true)
a × 1 = a and a ÷ 1 = a (true) point.
Inverse: If y = ax2 + bx + c has no minimum point, then
8. (a) 1 m2 = 10 000 cm2 and 1 cm3 = 1 000 mm3 /
1 m2 = 10 000 cm2 or 1 cm3 = 1 000 mm3 a < 0.
Contrapositive: If a < 0, then y = ax2 + bx + c has no
(b) 15 is a multiple of 5 or a perfect square.
minimum point.
(d) Converse: If x = a is one of the roots, then (x – a)(x – b) = 0.
Inverse: If (x – a)(x – b) ≠ 0, then x = a is not one of the

roots.
Contrapositive: If x = a is not one of the roots, then

(x – a)(x – b) ≠ 0.

337

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