2016 Yr 10 Bridging Course PDF

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Math Methods bridging course ...

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BRIDGING COURSE LEADING TO MATHS METHODS 1 & 2 CAS Ch. 2: Linear alge algebra bra and linear relations 1 Simplify by collecting like terms: 2

a) 7h – 3j + 4h – 2 j

4

2

b) 4fg – 5g f + 4fg – fg

3

2

4

3

2

c) 5n m – 4m n – 3n m + 6n m

2 Simplify the following: a) – 2s

2

 5d

7

b) – 2g

2

 3g

5

c) 6h i

4

4

 -3h i

d) 8uv  6ug

3 Expand and Simplify: a) -5(-2 – c) e) 4

2

3







4

2  



2

d) -5l  3l – 3l – 6 

-2(s – 5n – 3)

c)

f) 3c  2c – c  – 2c  3c + 4c

5(4x – 3) – 3(3x – 3)

2

3

2



g) d (2d – 4) + d  3d – 4d 

Factorise: 2

a) 7x + 49 5

b) -6(f – 3d + 2)

2

b) 9x – 81 x

2

c) 3a b + ab

d) -2x y – 2xy – 4x

Find expressions in simplest form for the perimeter ( P) and area (A ) of these shapes.

6 Find exact expressions in simplest form for the perimeter ( P ) and area ( A ) of these shapes. Your answer may contain  or a surd. e.g.

7

2

Simplify the following:

a)

f)

3x – 4x -2x

j)

x – 1 1 – x 4 2

m)

1 9

– 2a 3

2

2

– 18ab 9ab

–

g)

c)

2x + 4  x x + 2 x

k)

n)

–

2 2

26x y

b)

2

13xy

2 5

h)

2x – 6 x – 3 5x – 20 x–4

+ 4a 15

o)

7 9

– 3 a

10a 2

30a b

d)

3 – 15x 7  1 – 5x 2

l)

p)

2

x + x x e)

9c – 18 -9

i)

a – 1  3 1 – a 3

5 15  3a + 4 -15a – 20 2 7

– 3 2c

1

x – 3

q)

4

–

x + 2 2

r)

6 5 + x – 3 3x – 4

3x + 1 2x + 1 + 5 5

6 5 – 2x – 1 x + 7 u)

t) 8. Simplify these expressions a)

a – b b – a

b)

x

d) (x – 2)

5 + 2 2 a a

2

–

c)

s)

2 – x x – 1 – 5 10

v)

2 7 – 3x – 1 1 – x

2 3 + 2 x + 1 (x – 1) 2

x x – 2

x x – 2 2(3 – x) 7(x – 3) e)

.

1 – 1 – 1 z f) x y

9. By first simplifying the left – hand side of these equations, find the value of a. 2 4 a – = x – 1 x – 1 (x – 1) ( x + 1)

a) 10 Solve the following equations: b) -4x – 7 = 5 a) 5x + 4 = -10 e)

2(2x – 3) + 3(4x – 1) = 23

h)

2x – 6 = -10 5

l) 11 a) b) c) d)

3x – 5 = 2x – 8 4 3

i)

c) 6 – 7x = -12

f) 5(2x + 1) – 3(x – 3) = - 20

7 – 4x = 3 5

m)

b)

a 2 3 + = 5x + 2x – 1 x + 1 (2x – 1) ( x + 1)

j)

3x – 2 = 4 4

2 – x -2(x – 1) = 3 4

n)

2(3x – 4) = -6x

d)

g) 4(4x – 1) = 5(2x + 3)

k)

2 + x + 4 = -2 3

3(6 – x) = -2(x + 1) 2 5

For each of the following statements, write an equation and solve it to find x.

If 5 is subtracted from x the result is 5. Twice the value of x is added to 3 and the result is 9. 5 less than x doubled is -15. 5 less than twice x is 3 less than x.

12 The perimeter of an isosceles triangle is 42 mm. If the similar sides are 10 mm, determine the length of the odd side. 13 I ride four times faster than I walk. If a trip took me 45 minutes and I spent 15 of these walking 3 km how far did I ride? 14 A service technician charges $40 up front and $58 for each hour she works. a What will a 4-hour job cost? b If the technician works on a job for 3 days and averages 6 hours per day, what will be the overall cost? c Find how many hours are worked if the cost is: i $98 ii $649 iii $1000 (round to the nearest half hour) 15 The capacity of a petrol tank is 71 litres. If it initially contains 5 litres and a petrol pump fills it at 3 litres per 10 : seconds, find: a the amount of fuel in the tank after 2 minutes b how long it will take to fill the tank to 23 litres c how long it will take to fill the tank 16 Solve the following equations by multiplying both sides by the LCD .

2

3x a)

17

= 1 – 2x 3 5

x + 3 b)

3

– 4 = 4 + x 2

7 – 2x c)

3

– x = 1 – 6 2

Make “a” the subject in these equations. a)

a(b + 1) = c

d)

a – b = 1 b – a

b) ab + a = b 1 + 1 = 0 b a e)

1 + b = c c) a 1 + 1 = 1 a b c f)

COPY key ideas and STUDY the examples of the following pages: 58, 59, 61, 62, 63, 56, 66, 69, 70, 75, 76, 78. Area of study 1: Ch. 2: Linear algebra and linear relations Questions Ex. 2D: Solving linear inequations (pg 59) Q1, Q2: c, f, i, g, j Q4: c, e Q6 Ex. 2E: Graphs of linear equations (pg 63) Q1: a, c, f, j, k Q2: b, e, g, h Q3: e, f Q4: a, b, d, f, i, j Q5, Q8 Ex. 2F: Equations of lineaar graphs (pg 66) Q1 c, g, Q2: a, c, e, f Q3: c, d, e Q4: c, f, Q7 Ex. 2G: Solving simultaneous equatios graphically (pg 70) Q1: e, g, h Q2: c, g, h Q3: c, f, i Q4, Q6 Ex. 2H: Solving simultaneous equations algebraically (pg 76) Q1: j, l Q2: h, j Q3: d, f Ex: 2I: Applications of simultaneous equations (pg 79) Q1, Q2, Q5, Q6, Q7: c Q9, Q10 ************************************************************************************ COPY key ideas and STUDY the examples of the following pages: 243, 244, 246, 247, 249, 250, 252, 254, 257, 260, 262, 263, 265, 267, 268. Area of study 2: Ch. 6: Quadratic expressions Questions Ex.6A: Expanding quadratic expressions (pg 244) Q1: c, f, l, o Q2: f, l, o Q3: c, f, l, o, r, u Q4: b, f, j Q5: a Ex.6B: Perfect squares and DOPS (pg 247) Q1: d, h Q2: c, d, g, h Q3: c, f Q4: c, f Q5: b, d Q6: b, c Q7: b Ex. 6C: Factorisation including DOPS and perfect squares (pg250) Q1: a, d, g, h Q2: a, d, g Q3: b, f, j Q4: b, f, j Q5: c, f, i Q6: c, f, i Q7: b, f 2

Ex. 6D: Factorising quadratic trinomials of the form x + bx + c (pg 253) Q1: c, f, i, l Q2: c, f, i, l Q3: c, f, i, l Q4: c, f, i, l Q5: c, f, l 2

Ex. 6E: Factorising quadratics of the form ax + bx + c (pg 255) Q1: a, c, i Q2: a, c, f, i Q3: c, f, i Q4: a, c, d Q5 Ex. 6F: Multiplication and division of algebraic fractions (pg 258) Q1: b, e Q2: b, d, f Q3: b, d, f Q4: d, h, l Q5: d, h, l Q6: b, d Q7: b Ex. 6G:Factorising by completing the square (pg 261) Q1: b, d, Q2 c, f, i Q3: d, h Q4: c, f Q5: c, f Ex. 6H: Solving quadratic equations and the null factor law (pg 263) Q1: d, f, k Q2: c, f Q3: b, f Q4: b, f, h Q5: b, d, Q8 Ex: 6I: Solving quadratic equations by completing the square (pg 265) Q1: b, h Q2: b, d Q3: b, f Ex. 6J: Solving quadratic equations using the quadratic formula (pg 269) Q1: c, f, h, k Q2: c, f, i, l. ************************************************************************************* COPY key ideas and STUDY the examples of the following pages: 333, 334, 338, 342, 345, 346, 348, 349, 351, 352, 354, 357. Area of study 3: Ch. 8: Quadratic graphs Questions Ex. 8A: Plotting quadratic graphs (pg 336) Q1: a – f, Q2: a, b, c, e, i Q3: a, c, e Q4: a, b, c. 2

Ex. 8B: Investigating the transformations of f (x) = x (pg 339) Q1: a – f Q2, Q3: a – d Q5: a – d. Ex. 8C: Sketching with transformations (pg343)Q1:a, b, h, i, k Q2: a, b, c Q3. Ex. 8D: Sketching quadratic graphs using factorisation (pg 346) Q1: a, c, i Q2: a, f, g, l. Ex. 8E: Sketching quadratic graphs using turning – point form (pg 349) Q1: a, c, e, g Q2: a, d, e, f, l. Ex. 8F: Sketching quadratic graphs using the quadratic formula (pg 353) Q1: a, d, g, j, l Q2: a, d, g, h Q3: a, e, i, k. Ex. 8G: Applications of quadratics (pg 355) Q1, Q2. Ex. 8H: Modelling with quadratics (pg 358) Q1, Q2, Q5: b. *******************************************************************************************************************************

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PRACTICE ON THE USE OF CAS TO BE DELIVERED TO THE RECOMMENDED STUDENTS FROM WEEK 4 – 6

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