Revision questions
21A Core skills 1. 4x − y + 22 = 0 2. (0, −4) 3. (i) y = 6x + 7 (ii) x + 6y + 7 = 0
4. (i) (1 _
2, 5 _
(ii) 5√
_ 2
2)
(iii) x + y − 3 = 0 (iv) x + y − 2 = 0
5. Triangles are similar 6. (i) 3
(ii) x-intercept = (2 __
3, 0); y-intercept = (0, −2)
(iii) (2, 4) on the line; (−1, 5) not on the line
(iv) –14 (vi) (2, 4)
7. –5 8. (i) 3x + 7y − 15 = 0 (ii)
(−2, 3) (iii) Second missile can exit the hatch
9. (i) Equation of l: y = 4x − 3; slope of m= 1
(ii)
o = 3; y-intercept of o = 5 l, it has the highest slope
10.(i) 2x + 5y + 8 = 0 (ii) 5x − 2y − 13 = 0
21B Taking it further 1. (i)
(−4, −2)
(ii) 2 (iii) x + 2y + 8 = 0
2. (i) 3x − 4y + 16 = 0 (ii) W is on t (iii) [WZ]∥[XY] and [WX]∥[ZY]
3. (i) (2, 2)
(ii) (0, 1) (iii) W is on k (iv) √
_ 5 = √
_ 5
5. (i)
4. (i) C = (−5, 0); D = (4, 0) (ii) (0, 3) (iv) 13⋅5 square units (0, −1)
6. (ii) y-intercept represents the power in the battery when the laptop is turned on; x-intercept represents the number of hours it takes the battery to reach zero power
(ii) x − y − 1 = 0 (iii) s is on the line (iv) |QS| = |PS|
7. Lines are not perpendicular 8. (i)
(iii) 1 hr 15 mins t is on line m
(ii) 2x + y − 10 = 0 (iii) 3
9. (i) (−3, 5)
__ 2
(ii) (0, 4) (iii) 2x + y + 1 = 0 (iv) x – 2y + 8 = 0
)(m2) ≠ −1
__ of 2; y-intercept of n = 7; slope
(iii) No, it doesn’t satisfy the equation of n
(iv) No, the slopes are not the same (v) No, (m1
2. (a)
(v) PQRS is a square because the lengths of the sides are equal, the diagonals intersect at 90 degrees, opposites sides are parallel, sides are at right angles to each othermidpoint of PR = midpoint of SQ
Unit 22 Linking Thinking
revision material 1. (a)
(i) 8 seconds (ii) 260 m (iii) 112 m (iv) 112 m (v) The equation (vi) 0 to 1 second, as the graph is steeper in this region
(vii) 2.6 sec, 5.4 sec
(b) (i) 2 800 cm3 (ii) 2⋅2 cm
(ii) 13 units (iii) 5
(iv) 5x − 12y + 7 = 0
__ 12
(b) (i) Proof (ii) 23° (iii) Three interior angles of a triangle sum to 180°; 67° ; areas of the two
(c) 3. (a) (ii) 30 units2 (i) 4⋅5π cm2
triangles are equal , 12⋅5π cm2
, 8π cm3
(ii) Area of the sum of the smaller semicircles equals the area of the large semicircle
(iii) Pythagoras’s theorem
(b) €38 400 (c)
(ii) 9 cm (iii) 9⋅6 cm
5. (a)
4. (a) €18 895⋅68 (b) €24 000 (c) 5 years (i) 2x2
(ii) 8.16 × 108
(b) (i) 3⋅5 m (ii) 0⋅5 m (iii) 0⋅75 m (iv) 12 times
6. (a)
(i) 4π m2 (ii) Area of brick, in terms of π (m2
): 0, 4π, 16π, 36π, 64π, 100π
(iv) 9π m2 (v) Linear, same first difference (vi) Quadratic, second differences are equal
(b) (i) 53° (ii) 110° (iii) 90°
7. (a)
(i) €6 171⋅76 (ii) €2 671⋅76 (iii) €631
(b) (ii) Exponential, doubling eachweek
(iii) 18⋅2 km/h (c) + 5x − 3 cm3 (iii) 816 000 litres
8. (a)
(i) 6 cm (ii) Yes, they are similar (iii) 22·6° (iv) 2⋅5 cm
(b) (ii) 47⋅5° 9. (a)
(i) 8 000 cm3 (ii) 460 cm3 (iii) €19⋅20
(b) (i) Equilateral (ii) 10√
_ 3 cm
(iii) 37⋅3 cm 10.(a)
(i) Yes, angle is 74° (ii) 6⋅25 m
(b) (i) 1 680 cm3 (ii) 74 cm, 44 cm, 22 cm (iii) 1.1704 × 104
cm2 (c) 11.(a)
(i) 4 cm, 6 cm (ii) 442 mm
(i) 6, 8, 10; 9, 12, 15 (ii) No, because the sum of two odd numbers is always even
(b) (i) 5 (ii) 30 units2
(d) (i) 2√ (ii) 4√ (iii) 8√
12.(a)
_ 5
_ 3
_ 2
(i) F or G 13.(a)
(b) (i) 13° (ii) 6⋅7 m (iii) 14⋅74 m2 (iv) 2 rolls (v) 26⋅3% (i) 5x2 (ii) 5
+ 5x
(b) (i) 77° (ii) 116°, 58° (iii) 90°
14.(a)
(i) A = €1 750, B = €32 800, C = €6 888, D = €5 138, E = €28 362
(ii) €545⋅42 (iii) Weekly pay will decrease;
weekly pay will decrease; weekly pay will increase; will have no effect on pay
(iv) €10 085
(b) (i) 5 units (ii) 19⋅6 units2 (iii) 2 (v) AB: x − 2y + 10 = 0; CD: 2x − y − 10 = 0
(vi) (10, 10) 15.(a)
(i) Quadratic, second differences are equal
(iii) 450 ± 10 km/hr (iv) More time to accelerate to the required speed to take off
(b) (i) 11 160 Kr (ii) 10 881 Kr
(i) 6 m2 (ii) 5x − x2 (iii) 6 − 5x + x2 (iv) 2x2
(v) 0.32 m − 10x + 3 = 0
390
Linking Thinking 2
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