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Department of Mathematics and Applied Mathematics Departement Wiskunde en Toegepaste Wiskunde GRADES 8 AND 9 GRADE 8 EN 9 27-31 July 2020 27-31 Julie 2020 TIME: 2 HOURS TYD: 2 URE No calculators. Geen sakrekenaars. ©2012 OUTEURSREG VOORBEHOU, UNIVERSITEIT VAN PRETORIA ©2012 COPYRIGHT RESERVED, UNIVERSITY OF PRETORIA

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Page 1: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Department of Mathematics and Applied Mathematics

Departement Wiskunde en Toegepaste Wiskunde

GRADES 8 AND 9 GRADE 8 EN 9 27-31 July 2020 27-31 Julie 2020 TIME: 2 HOURS TYD: 2 URE No calculators. Geen sakrekenaars.

©2012 OUTEURSREG VOORBEHOU, UNIVERSITEIT VAN PRETORIA ©2012 COPYRIGHT RESERVED, UNIVERSITY OF PRETORIA

Page 2: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Question 1 Vraag 1

Arrange the numbers x− 1, x + 2, x− 7,x + 5, and 2x − (3 + x) from smallest tobiggest. What is the middle number?

Ranskik die getalle x−1, x+2, x−7, x+5,en 2x − (3 + x) van kleinste na grootste.Watter getal is in die middel?

(A) x− 1 (B) x + 2 (C) x− 7 (D) x + 5 (E) 2x− (3 + x)

Question 2 Vraag 2

If 6a + 3b = 9 and 3a − b = 7, then whatis a?

As 6a + 3b = 9 en 3a − b = 7, wat is adan?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Question 3 Vraag 3

If a ./ b =a

b+

b

a, then 1 ./ 2 + 2 ./ 3 is

equal to?

As a ./ b =a

b+

b

a, dan is 1 ./ 2 + 2 ./ 3

gelyk aan?

(A)14

3(B)

7

3(C)

7

6(D)

7

2(E) 1

Question 4 Vraag 4

Calculate1

1 + 11+ 1

2

Bereken1

1 + 11+ 1

2

(A)1

2(B)

3

5(C)

5

3(D)

2

3(E)

3

2

Question 5 Vraag 5

How many positive integers less than 100are simultaneously multiples of 2, 3, and4?

Hoeveel positiewe heelgetalle kleiner as100 is gelyktydig veelvoude van 2, 3, en4?

(A) 1 (B) 3 (C) 6 (D) 7 (E) 8

Question 6 Vraag 6

You pick a whole number, multiply it byfive, and then divide it by two. The result-ing number is an odd number, less thanten. What was the number you picked?

Jy kies ’n heelgetal. Jy maal die getalmet vyf en deel dit dan deur twee. Diefinale getal is ’n onewe getal, minder astien. Wat was die getal wat jy gekies het?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

1

Page 3: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Question 7 Vraag 7

Winnie wants to calculate the circumfer-ence of a circle with radius r = 3 cm.However, Winnie doesn’t know the for-mula for the circumference of a circle.She decided to approximate the circum-ference by inscribing a hexagon in the cir-cle and determining the circumference ofthe hexagon. What is the circumferenceof the hexagon?

Winnie wil die omtrek van ’n sirkel metradius r = 3 cm bereken. Winnie kenegter nie die formule vir die omtrek van’n sirkel nie. Sy besluit om die omtrek teskat deur ’n seshoek in die sirkel te tekenen die omtrek van die seshoek te bepaal.Wat is die omtrek van die seshoek?

r

(A) 10 cm (B) 12 cm (C) 14 cm (D) 16 cm (E) 18 cm

Question 8 Vraag 8

When a water tank is 75% full, it contains200 litres more water than when it is 25%full. How many litres does the water tankhold when it is full?

As ’n watertenk 75% vol is, bevat dit 200liter meer water as wanneer dit 25% volis. Hoeveel liter hou die watertenk as ditvol is?

(A) 300 (B) 400 (C) 500 (D) 600 (E) 700

Question 9 Vraag 9

A 30 cm stick casts a shadow which is 40cm long. At the same time a tree has ashadow which is 12 m long. How tall isthe tree?

Die skaduwee van ’n 30 cm stok is 40cm lank. Terselfdertyd het ’n boom ’nskaduwee wat 12 m lank is. Hoe lank isdie boom?

(A) 6 m (B) 7 m (C) 8 m (D) 9 m (E) 10 m

2

Page 4: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Question 10 Vraag 10

In the diagram below, ABCD is a squareand CDE is an equilateral triangle. Findx (that is, the angle ACE).

In die onderstaande diagram is ABCD ’nvierkant en CDE ’n gelyksydige driehoek.Bepaal x (dit wil se die hoek ACE).

A B

CD

E

x

(A) 15◦ (B) 20◦ (C) 25◦ (D) 30◦ (E) 35◦

Question 11 Vraag 11

Boat A is traveling east at a speed of 6km/h and Boat B is traveling north at 8km/h. If the distance between the boatswill be 0 km in 10 hours time, what willthe distance between them be in 5 hourstime?

Boot A reis ooswaarts met ’n snelheid van6 km/h en Boot B ry noordwaarts teen 8km/h. As die afstand tussen die bote in10 ure 0 km sal wees, wat sal die afstandtussen die bote in 5 ure wees?

(A) 10 km (B) 20 km (C) 30 km (D) 40 km (E) 50 km

Question 12 Vraag 12

If a equilateral triangle with perimeter Phas area A, then an equilateral trianglewith perimeter 1

3P has what area?

As ’n gelyksydige driehoek met omtrek P’n oppervlakte van A het, wat is die op-pervlakte van ’n gelyksydige driehoek metomtrek 1

3P?

(A)2

3A (B)

5

9A (C)

1

3A (D)

1

6A (E)

1

9A

3

Page 5: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Question 13 Vraag 13

Kamogelo looked at his watch and noticedthat, at that moment, it was 6x minutesafter 14:00 and 9x minutes before 15:00for some value of x. What time was it atthat moment?

Kamogelo kyk na sy horlosie en let op datdit 6x minute na 14:00 was en 9x minutevoor 15:00 was vir ’n sekere x. Watter tydvan die dag was die oomblik?

(A) 14:24 (B) 14:28 (C) 14:32 (D) 14:36 (E) 14:40

Question 14 Vraag 14

A train travels for 10 kilometers at a speedof 60 km/h and then the next 10 kilome-ters at 80 km/h. What is its average speedof the train over the 20 kilometer journey?

’n Trein ry 10 kilometer met ’n snelheidvan 60 km/h en nog 10 kilometer teen80 km/h. Wat is die gemiddelde snelheidvan die trein gedurende die 20 kilometerrit?

(A) 70 km/h (B)√

4800 km/h (C) 72 km/h (D)480

7km/h (E) 75 km/h

Question 15 Vraag 15

The letters A, B, C, and D are to be placedin the grid so that each of these letters ap-pears exactly once in each row and exactlyonce in each column. Which letter will goin the square marked with ∗?

Die letters A, B, C, en D word in dievierkant ingevul sodat elkeen van die let-ters presies eenkeer verskyn in elke ryen presies eenkeer verskyn in elke kolom.Watter letter sal in die vierkant gemerkmet ∗ verskyn?

A DB C* C B

B D AA E

(A) A (B) B (C) C (D) D (E) E

Question 16 Vraag 16

The price of a certain ice-cream increasesby 10% each year. If the price in 2020 isR11.00, what was the price in 2018?

Die prys van ’n sekere roomys verhoog elkejaar met 10%. As die prys in 2020 R11.00is, wat was die prys in 2018?

(A) R8.80 (B) R8.91 (C) R8.99 (D) R9.00 (E) R9.09

4

Page 6: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Question 17 Vraag 17

Sally throws two normal six-sided dice.What is the chance that the sum of theresults add up to a prime number?

Sally gooi twee normale seskantige dobbel-stene. Wat is die kans dat die som van dieresultate ’n priemgetal is?

(A)16

36(B)

15

36(C)

14

36(D)

13

36(E)

12

36

Question 18 Vraag 18

Alex and Alicia write six tests in onesemester. They both get 80% for the firstfour tests. Alex gets 90% and 100% forthe last two tests. If Alicia average forall six tests is 10 percentage points lessthan Alex’s average, then what is the low-est mark Alicia could possibly have gottenfor one of the last two tests?

Alex en Alicia skryf ses toetse in eensemester. Hulle kry albei 80% vir dieeerste vier toetse. Alex kry 90% en 100%vir die laaste twee toetse. As Alicia segemiddeld vir al ses toetse 10 persen-tasiepunte minder is as Alex se gemiddeld,wat is die laagste punt wat Alicia vir eenvan die laaste twee toetse kon behaal het?

(A) 15% (B) 20% (C) 30% (D) 50% (E) 65%

Question 19 Vraag 19

John, Lethabo and Mpho always wear ei-ther red, blue, or yellow shirts. No two ofthem ever where the same colour on thesame day. Additionally,

1. If John wears a blue shirt, thenMpho wears a yellow shirt.

2. If Lethabo wears a yellow shirt, thenJohn wears a red shirt.

3. If Mpho wears a yellow shirt, thenLethabo wears a blue shirt.

So it is possible that John could wear ayellow shirt, Lethabo could wear a redshirt, and Mpho could wear a blue shirton the same day. This would be one possi-ble colour combination. How many colourcombinations are possible in total?

John, Lethabo en Mpho dra altyd rooi,blou of geel hemde. Geen twee van hulledra ooit dieselfde kleur op dieselfde dagnie. Verder:

1. As John ’n blou hemp dra, dan draMpho ’n geel hemp.

2. As Lethabo ’n geel hemp dra, dandra John ’n rooi hemp.

3. As Mpho ’n geel hemp dra, dan draLethabo ’n blou hemp.

Dit is dus moontlik dat John ’n geel hempkon dra, Lethabo ’n rooi hemp kon dra,en Mpho ’n blou hemp kon dra op die-selfde dag. Dit is een moontlike kleurkom-binasie. Hoeveel kleurkombinasies is in to-taal moontlik?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

5

Page 7: u v } ( D Z u ] v o ] D Z u ] u v t ] l µ v v d } P t ] l µ v · u v t ] l µ v v d } P t ] l µ v 'Z ^ ô E õ 'Z ô E ... If a equilateral triangle with perimeter P has area A,

Question 20 Vraag 20

Karabo goes for a walk. She starts by tak-ing one step east. She then takes two stepsnorth. Then she takes three steps east.She then takes four steps north. If shecontinuous this way she will have walkedeight steps north after she had walked 17steps in total. How many steps north willshe have given after she has walked 817steps in total?

(Hint: start by calculating how manysteps (i) in total, (ii) east, and (iii) northshe has given if she has given 1 + 2 + 3 +4 + 5 + · · ·+ 2n steps in total.)

Karabo gaan stap. Sy begin met een treeoos. Sy neem dan twee tree noord. Danneem sy drie tree oos. Sy neem dan viertree noord. As sy so voortgaan, sal sy agttree noord geloop het nadat sy altesaam17 tree geloop het. Hoeveel tree noord salsy gegee het nadat sy ’n totaal van 817tree gestap het?

(Wenk: begin met die berekening van hoe-veel tree (i) in totaal, (ii) oos, en (iii)noord sy gegee het as sy in totaal 1 + 2 +3 + 4 + 5 + · · ·+ 2n tree gegee het.)

(A) 397 (B) 400 (C) 417 (D) 420 (E) 423

6


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