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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
