Williamwood High School

MATHEMATICS

ADVANCED HIGHER

GEOMETRY AND PROOF

HOMEWORK & CONSOLIDATION

BOOKLET

S6 Daily Homework Geo & Proof Week 1

Monday/Tuesday

1. Expand

2. Find the 100th term of the arithmetic

sequence 10, 12, 14, 16…

3. Differentiate

Wednesday

1. Expand

2. Find the 16th term of the arithmetic

sequence 1, 4, 7, 10…

3. Differentiate expressing

in fully factorised form

Thursday/Friday

1. Expand

2. Find the sum of the arithmetic series

2+6+10+14+ , to 30 terms

3. Differentiate

S6 Daily Homework Geo & Proof Week 2

Monday/Tuesday

4. Use Gaussian elimination to solve each

set of linear equations for x, y and z

(a) x + y + z = 10

2x + 3y + z = 21

x + 2y + 4z = 19

(b) x + y + 2z = 9

3x + 4y + z = 18

2x + 3y + 2z = 15

Wednesday

4. Use Gaussian elimination to solve each set

of linear equations for x, y and z

(a) x + 2y + z = 12

2x + 5y + 4z = 36

2x + 6y + 3z = 33

(b) x + y + 2z = 4

3x + 4y + z = 19

2x + y + 4z = 6

Thursday/Friday

4. Use Gaussian elimination to solve each

set of linear equations for x, y and z

(a) x + 2y + z = 14

x + 3y + 3z = 24

2x + 3y + z = 22

(b) x + y - z = 1

2x + 3y + z = 13

x + 2y - 2z = 0

S6 Daily Homework Geo & Proof Week 3

Monday/Tuesday

Find each matrix product;

(a)

(b)

(c)

Wednesday

Find each matrix product;

(a)

(b)

(c)

Thursday/Friday

Find each matrix product;

(a)

(b)

(c)

S6 Daily Homework Geo & Proof Week 4

Monday/Tuesday

5. If A= then find det A

6. a = i + 2j + 3k and b = 2i – j + k

find a x b

Wednesday

5. If A= then find det A

6. b = i + k and c = 2i – j + 3k

find b x c

Thursday/Friday

5. If A= find A-1

6. Find the symmetric form of the

equation of the line through (6,3,-5) in

the direction

S6 Daily Homework Geo & Proof Week 5

Monday/Tuesday

7. Find the Cartesian equation of the plane

containing A(0,1,-1), B(1,1,0) and C(1,2,0)

8. Plot z = 5 +12i, and find both the

modulus and argument.

Wednesday

7. Find the Cartesian equation of the plane

containing point P(3,-2,-7) and the line

8. Plot z = 5-2i, and find both the modulus

and argument.

Thursday/Friday

7. Find the point of intersection of the line

and the plane

6x+4y-5z=28

8. Let z = 2(cos700 + isin700) and

w = 6(cos300 + isin300);

express in the form r(cosθ + isinθ)

(a) zw (b) (c) z2

S6 Daily Homework Geo & Proof Week 6

Monday/Tuesday

9. Find the GCD of 1989 and 867

10. Convert 3910 to base 2.

Wednesday

9. Find the GCD of 987 and 144

10. Convert 36610 to base 5.

Thursday/Friday

9. Find the GCD of 1365 and 299

10. Convert 34710 to base 8

S6 Daily Homework Geo & Proof Week 7

Monday/Tuesday

11. It is suggested that n2+n, where n is a

positive integer, gives an answer that is

always a multiple of 3. Is the conjecture

true or false, explain

12. Prove by Induction

Wednesday

11. Disprove the conjecture that x+x2≥0

for xєR

12. Use proof by contradiction to show that

if m2 is odd then m is odd.

Thursday/Friday

11. Prove that if n5 is odd then n is odd

using proof by contrapositive

12. Prove by Induction

ADVANCED HIGHER GEOMETRY AND PROOF

HOMEWORK 1

1.

2.

3.

ADVANCED HIGHER GEOMETRY AND PROOF

HOMEWORK 2

1. Solve z2 + 2z + 5 = 0 and represent the solutions on an Argand diagram.

2. Verify that z = 1 + i is a root of the equation z4 + 3z

2 – 6z + 10, and find the

other roots.

3. Interpret geometrically in the complex plane the equation iz 3 = 1z

4. Expand 4sincos i using the binomial theorem and De Moivre’s theorem.

Use your expansion to express 4cos as a polynomial in cos .

5.

6.

7.

Geometry, Proof and Systems of Equations Assessment Practice 1

Geometry, Proof and Systems of Equations Assessment Practice 2

Geometry, Proof and Systems of Equations Assessment Practice 3