HOW TO PASS NATIONAL 5 MATHS

Size: px

Start display at page:

Download "HOW TO PASS NATIONAL 5 MATHS"

Griselda Malone
5 years ago
Views:

1 HOW TO PASS NATIONAL MATHS Name: Homework 9 0 Score

2 Homework Sheet Evaluate Find the equation of the straight line passing through these points: (,-) and (,9). Simplify m x m -9 Change the subject of the mn formula to m: k p Solve sinx o = (for 0< x <0) Find the mean and standard deviation for this data:,,,, Factorise fully: t A classic car bought for,000 increases in value by.% every year for years. Its new value? Is a triangle with sides cm, 0cm and cm right-angled? Find the roots of the equation y = x - x -

3 Homework Sheet Evaluate. +. x 0 Find the equation of the given straight line. Simplify 0 Change the subject of the r formula to r: p y Solve tanx o + = (for 0< x <0) Solve this equation to d.p. x + x = 0 Factorise fully: x + 9x - 0 A bottle contains ml which is 0% more than it used to. What was the original volume? 9 Find the value of x: 0 Find the roots of the equation y = x - 9x -

4 Homework Sheet Find Find the equation of a straight line through (,-) parallel to y=x+. Remove brackets and simplify a a Solve x -(x+) = 9 0 Sketch the graph of y=cosx o for0 x 0 Find the volume of a sphere with radius cm, giving your answer to two significant figures. Remove brackets and simplify (x + ) (x - ) Dave s car was bought for,000 but is losing.% each year. What will it be worth in years? Triangle ABC has AC=.m, angle ABC= o and angle ACB=0 o. Find the length of AB. Describe the nature of the roots of y = x - x -

5 Homework Sheet..x Without a calculator: Does the point (-,) lie on the line y = x +0? Explain your answer. Simplify, leaving your answer as a surd: 0 Simplify (x + )(x -) Sketch the graph of y = sin(0.x o ) for 0 x 0 Solve x -x+=0, giving your answers to two decimal places. Factorise x -x In a Spring Sale, a bag of springs now costs.0. What was it worth before the 0% sale? What is the area of an equilateral triangle of side 0cm? Sketch y = (x - )(x+). Label the intercepts and turning point.

6 Homework Sheet If f(x) = x + x, find f(-) Which of these could this line represent? A: y = x + B: y = -x + C: y = x D: y = x - E: y = -x - Find the length of the longest side on a right angled triangle with smaller sides cm and cm (leave your answer as a simplified surd). Solve x ( x) 9 0 Solve tanx o = (for 0< x <0) Calculate the standard deviation for this:,,, 0 Expand and simplify (x+)(x -x+) China s population is.x0 9. If this increases by % for the next years, what will it be? A square has side x. It has a diagonal of cm. Calculate the exact length of x. How many real solutions are there to the equation x x + = 0?

7 Homework Sheet Find 9 A straight line with gradient passes through (,) and (,a). Find the value of a. Expand k k k k Change the subject of the formula to W: W J L This is the graph y=asin(bx o ) Find the value of a and b. Can a cylinder with height 0cm and diameter cm hold 00ml of water? Explain your answer. Factorise fully: 0x - 0x My total bill for fixing my car included % tax. If the bill was, what was the bill before tax? A triangle has sides cm, cm and cm. Find the sizes of its biggest angle. Sketch y = (x - )(x +.) Label the intercepts and turning point.

8 Homework Sheet Without a calculator find to three decimal places. What is the equation of this line? Solve Find x x What is the value of a in this graph y =cos(ax o ) Show that the standard deviation of,,,, is and write down the s.d. of 0,0,0,0,0. Multiply out and simplify: (x - x +) x(x ) If these shapes have the same height which has greater volume: a cone with radius cm or a cylinder with radius cm? 9 Here s the Bermuda Triangle (Bermuda- Miami-Puerto Rico). Find angle BMP 0 Write down the axis of symmetry and the coordinates of the turning point of y = (x-) +

9 Homework Sheet Without a calculator find % of.0 A straight line is given by y=mx+c. Sketch this to illustrate a possible graph when m > 0 and c < 0. ab Simplify a b Write as a single fraction a a Solve sinx o = sinx o + for 0 x 0 Solve x + x = 0, giving your answer to two decimal places. Factorise Can you use your answer to see what the value of this expression is? 9 The big jar of marmalade (0g) has.% more than the standard one. What s in the standard one? Plot the point A (-,) on a coordinate diagram. How far is it from A to the origin? 0 Here is the graph of y=(x-a) +b Find a, b and use your equation to find c.

10 Homework Sheet 9 Find the mean of,,,. Find the gradient and y-intercept for this straight line: x + y = Express with a rational denominator in its simplest form. Change the subject of the formula to h: A ha b The graph shown is y= sinx o -. Find the coordinates of Q and P. M Test Scores: Mean=%, s.d.=0% M Test Scores: Mean=9%, s.d.=% Give two valid comparisons. Factorise fully y - 0y - A patient gets 0mm of a drug at pm. Every hour the amount of blood decreases by 0%. How much is in the blood at pm? 9 Find the length of SW. 0 Describe the types of roots this quadratic has: y = x + x

11 Homework Sheet 0 Jamie is baking cakes for a party. Each cake needs block of butter. If he has blocks of butter how many cakes can he make? Find the equation of a straight line between (-, ) and (-,-). Express p p p in simplest form. Solve for x: ( x ) x Solve sin x for 0 x 0 A cuboid has a volume of.9m. It has a length of 0cm and a breadth of 0cm. Find the height. Multiply out and simplify: (x+) My microwave cost 0 (includes.% VAT). How much did it cost before VAT was added? 9 Find the length of AB. 0 This garden has an area of m. Find x.

12 Summary Keep a record of the questions that you are getting right. Use this to identify the areas where you are struggling a bit. Ask your teacher for help with these areas! 0: Quadratics (Solving, Graphs) 9: Triangle Rules (Pythagoras, Sine Rule, Cosine Rule, Area of Triangle) : Percentages (including compound interest, appreciation, depreciation, working backwards) : Factorisation and Multiplying Out Brackets : Using formula (including standard deviation, quadratic formula and volumes) : Trigonometric graphs and equations : Algebra (including changing the subject of a formula, solving equations and inequations) : Surds and Indices : Equation of a straight line : Basic calculations (including fractions and BODMAS) Homework 0 Homework 9 Homework Homework Homework Homework Homework Homework Homework Homework

Mark = / Exam Questions. My Working. 1 Evaluate. 2 Find the equation of the line. 3 Express. in its simplest form. 4 Solve.

Mark = / Exam Questions. My Working. 1 Evaluate. 2 Find the equation of the line. 3 Express. in its simplest form. 4 Solve. 100 Exam Questions 1 Evaluate Mark = /10 My Working 6 1 5 2 1 3 2 Find the equation of the line 3 Express a 2 (2a 1 2 + a) in its simplest form 4 Solve x 2(x 1) = 8 5 Solve 4sinx = 2 for 0 < x < 360 6