HILLEL ACADEMY HIGH 8th Grade

MATHEMATICS DEPARTMENT

INTEGERS, POWERS & ROOTS REVIEW

1. Find the value of each expression without using a calculator.

i) [ ( ) ( )]

ii)

iii) [ ( )]

( )

iv) ( )

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2. Write down one more multiplication fact and two division facts using the numbers

given in each of the following:

i)

ii) ( )

iii) ( ) ( )

3. Barry has an overdraft. He pays some off each month. He uses this formula to find the

amount still owing, N.

is the initial over draft, is the number of months and is the amount he pays each month.

Find if

i) D =

ii)

iii)

5. Which of the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, &10.

i) 585

ii) 864

iii) 2676

iv) 7002

6. Solve the following:

i) Use factor trees or a table to prime factorize:

a) 132 and 48

b) 144 and 720

c) 195 and 200

ii) Write all answers found in 6i in index notation.

iii) Represent all answers found in 6i in 3 different venn diagrams.

iv) Find the HCF and LCM for all answers found in 6i.

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7. Find the HCF and LCM of the following:

a) 36a and 12ab

b) 24p2qr and 36pqr

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c) 12wxz, 12wz, 24wxyz

8. i) What is inverse operation of square?

ii) Is √

positive or negative?

9. With the use of a calculator, solve the following and if needed round to 2d.p.:

i) 145

ii)

iii) ( )

v) √

vi)√

vii) √

+ √

iv) 2.82 + 3 × 4.6

2viii) √

10. Find these by factorizing.

i) √ ii) √

iii) √ iv) √

11. Without the use of a calculator, use the index laws to simplify these.

i) ii)

iii) iv)

v)

vi)

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Algebra Review

1. Simplify where possible.

a) b) ( ) c) ( ) ( ) d) ( ) ( ) e)

f)

g)

h)

i)

j)

k)

2. Factorize completely the following expressions:

a) b) c) d)

3. Solve the following equations.

a) b)

c) d) ( ) e) ( ) f) ( )

g) ( ) h) ( ) ( )

i) ( ) ( ) j)

k)

l)

m)

( ) n)

( )

( )

o)

p)

4. Evaluate each expression if

.

a) b)

c)

d)

e) f)

g) √ ( ) h) ( )

5. Translate each phrase into an algebraic expression.

a) three more than the number of cakes baked.

b) six feet shorter than the mountain’s height.

c) nine more than a number divided by six.

d) the difference of seventeen and four times a number

e) three times the product of twenty five and a number.

f) four less than twice a number

6. Translate each algebraic expression into words.

a) b)

c)

( ) d) ( )

7. Due to gravity, objects weight three times as much on Earth as they do on Mercury.

a) Suppose the weight of an object on Mercury is Write an expression for the object’s

weight on Earth.

b) How much would an object weigh on Earth if it weighs 25 pounds on Mercury?

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8. The selling price of a sweater is the cost price plus the markup minus the discount.

a) Write an expression to show the selling price of a sweater. Use for cost, for

markup, and for discount.

b) Suppose the cost of a sweater is $25, the markup is$20, and the discount is $6.

What is the selling price of the sweater?

9. During the month of July, meteorologists recorded 5 inches of rainfall. This is 6 inches

below average. Define a variable and write an equation that can be used to determine the

average rainfall for July. Find the average rainfall for July.

10. Megan purchased movie tickets for herself and two friends. The cost was $24.

a) Define a variable. Then write an equation that can be used to find how much

Megan paid for each ticket.

b) What was the cost of each ticket?

11. Bob is 7 years older than Jane. Two years from now he will be twice as old as Jane was last year. How old are

they now?

12. The sum of three consecutive even numbers is 105, what are the numbers?

13.

a) Write 3 different expressions for each of these shaded areas. Show your work.

b) Show in each case that your 3 expressions are equivalent.

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5

14.

a) Write 3 different expressions for each of these shaded areas. Show your work.

b) Show in each case that your 3 expressions are equivalent.

*WHEN FINISHED, COMPLETE PAGES 196-198 IN TEXTBOOK*

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Inequalities Review

1. Solve and check each inequality. Graph each solution on a number line.

a) b)

c) d) ( )

e)

f)

2. Solve and check each inequality.

a) b) ( )

c)

( ) d)

e) f)

g) h)

3. Graph each of the following on a Cartesian plane.

a) b)

c) c)

d) e)

3. The manager of Family Fare wants to set sandwich prices so that all members of a family of

four can each order a sandwich and a drink for less than $20.00. All drinks are priced at

$0.89.

Write and solve an inequality to find what prices the manager should set for the sandwiches.

4. Over the telephone, an electrician told Mrs. Watts that the labor required to repair the

electrical problem she described would cost at least $150. He said that this included a base

service call charge of $40 plus $25 per hour.

Write and solve an inequality to determine how many hours the electrician estimated for the repair.

5. Mark is placing a classified ad in his city’s newspaper to advertise his lawn care services.

Ads cost $0.75 per word. He wants to spend no more than $25.00 for the ad.

a) Write an inequality describing the number of words Mark could have.

b) Solve the inequality. How many words could Mark have in his ad?

6. Sam’s brother is three years more than twice his younger brother’s age. If the sum of their ages is at

most 18, then find the greatest age that Sam’s brother could be.

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Coordinate Geometry Review

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10

11

12.

13.

14.

12

15.

16.

17.

13

18.

19.

20.

14

21.

22.

15

23.

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MEASUREMENT Review

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SEQUENCES Review

ARITHMETIC SEQUENCE

1. For each of the following sequences find:

i. Find the next three terms

ii. Write a recursive formula

iii. Write the general formula

iv. Find 20th term

a.

b.

c.

d.

e.

f.

g.

2.

3. Find the position of 276 if it is in the sequence?

Find the position of 103 if it is in the sequence?

Find the position of 314 if it is in the sequence?

Find the position of -96 if it is in the sequence?

4. Find the formula for the nth term for each sequence by:

i. Write a formula to generate the numerators

ii. Write a formula to generate the denominators

iii. Combining the answers to part i. and ii. above to find the nth term

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GEOMETRIC SEQUENCE

5. For each of the following sequences find:

i. Find the next two terms

ii. Write a recursive formula

iii. Write the general formula

iv. Find 10th term

(e)

(f)

(g)

(h)

(i)

(j)

(h)

6.

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OTHER SEQUENCES

7. For each sequence of patterns:

a. find the next three terms

b. write a recursive formula

8.

9. For each sequence of patterns:

a. draw the next two shapes

b. write the formula for the nth term

c. find the number of dots in the 10th diagram

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10. For each of the following sequences write th formula for the nth term (general formula):

11. .

12. For each of the following sequences :

i. Find the next two terms

ii. Write the general formula for each sequence by:

1. Write a formula to generate the numerators

2. Write a formula to generate the denominators

3. Combining the answers to part 1. and 2. above to find the nth term

(f)