Lesson-5.1.4- Solve problems involving standard form. - Alai Academy

Chapter-5. Standard form (number)

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Lesson-5.1.1- Convert large and small numbers into standard form and vice versa. Write these numbers in standard form: 2 900 000 0.000 000 41 Write these as ordinary numbers: 5 × 10^4, 4.6 × 10^−3

Lesson-5.1.2- Order numbers written in standard form and/or include writing statements using inequality signs: >, <, , 

Lesson-5.1.3- Add, subtract, multiply and divide numbers in standard form. Enter and read standard form numbers on a calculator.

Lesson-5.1.4- Solve problems involving standard form.

Chapter-7. Equations (Algebra)

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Lesson-7.1.1- Find pairs of numbers that satisfy a linear equation with two unknowns. x + y = 7 Write down 2 possible values for x and y.

Lesson-7.1.2- Solve linear equations including unknowns on both sides. Solve 4x − 3 = 2x + 7, 5y + 4 = 7y + 5

Lesson-7.1.3- Solve linear equations, including unknowns on both sides and/or include brackets or fractions.

Lesson-7.1.4- Solve problems by writing and solving equations. A man said ‘My brother is 8 years’ older than me, my sister is 5 years’ younger than me, and all three of our ages add up to 129’. How old is the man’s brother?

Lesson-7.1.5- Solve equations involving an x² term and a number. Solve x² – 25 = 96

Lesson-7.1.6- Solve quadratic equations of the form x² + bx + c = 0, by factorizing. Solve x² − 7x – 30 = 0

Lesson-7.1.7- Write equations to represent direct proportion. When x = 16, y =4 y is directly proportional to x Write a proportionality equation involving x and y.

Lesson-7.1.8- Solve a pair of simultaneous linear equations. Solve the simultaneous equations: 2x + 3y = −4, 4x − y = 6

Lesson-7.1.9- Solve problems involving simultaneous linear equations or direct proportion. 4 burgers and 3 cakes costs $14.80 5 burgers and 2 cakes costs $15.70 How much would 6 burgers and 4 cakes cost?

Chapter-8. Sequences (Algebra)

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Lesson-8.1.1- Find the term-to-term rule of a sequence. 5, 9, 13, 17, 21, …

Lesson-8.1.2- Find terms of a sequence using a given term-to-term rule. A sequence starts with 8 and has a term-to-term rule of −3 What are the first 5 terms of the sequence? What is the 10th term of the sequence?

Lesson-8.1.3- Recognize different types of sequence. 2, 4, 6, 8, 10, … 2, 4, 8, 16, 32, … 1, 4, 9, 16, 25, … 1, 3, 6, 10, 15, … 1, 1, 2, 3, 5, 8, … 1, 8, 27, 64, 125, …

Lesson-8.1.4- Generate terms of a sequence using a position-to-term rule in context. The position-to-term rule of a sequence is: ‘Double the position number then subtract 1’ Find the first 5 terms of this sequence.

Lesson-8.1.5- Use the nth term to generate a linear or quadratic sequence. Find the first 5 terms of the sequences: 5n + 7 4n²

Lesson-8.1.6- Find the nth term of an arithmetic sequence. Find the nth term of the sequence: 2, 9, 16, 23, 30, …

Lesson-8.1.7- Recognize and continue more complex geometric sequences. Find the next term in the sequence: 1, 2.5, 5, 8.5, 13, …

Lesson-8.1.8- Solve problems involving sequences. Ali writes an arithmetic sequence that starts with: 4, 7, 10, 13, … Bhavin writes an arithmetic sequence that starts with: 15, 23, 31, 39, … Ali says that 111 is in both of their sequences. Is he correct? You must show your working.

Chapter-10. Inequalities (Algebra)

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Lesson-10.1.1- Understand and use the symbols: , ≤, ≥ | State the integers that satisfy −2 < x ≤ 5

Lesson-10.1.2- Represent solutions to linear inequalities on a number line. Solve linear inequalities with one unknown.

Chapter-13. Symmetry (Geometry)

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Lesson- 13.1.1- Recognize and describe order of rotational symmetry. Complete this diagram so that it has rotational symmetry order 4.

Lesson-13.1.2- Identify and describe all the symmetries of common 2-D shapes (reflection and rotational). Equilateral triangle, isosceles triangle, square, rectangle, parallelogram, rhombus, trapezium, kite, pentagon, hexagon, octagon, nonagon, decagon.

Lesson-13.1.3- Identify reflection symmetry in common 3-D solids

Chapter-14. Transformation (Geometry)

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Lesson-14.1.1- Translate 2-D shapes given a column vector.

Lesson-14.1.2- Use column vectors to describe translations. Describe the transformation that maps Shape A onto Shape B.

Lesson-14.1.3- Recognize and draw reflections in a mirror line. Reflect the shape given in the mirror line y=x

Lesson-14.1.4- Reflect a shape on a coordinate grid; describe a reflection on a coordinate grid. Reflect in the lines y =a, x= a, y =±x

Lesson-14.1.5- Describe and perform rotations about a Centre on a coordinate grid. Fully describe the transformation that maps Shape A onto Shape B (Centre, direction and amount of rotation).

Lesson-14.1.6- Enlarge shapes using positive, negative and fractional scale factors, about a Centre of enlargement.

Lesson-14.1.7- Describe the scale factor and the Centre of enlargement given an object and its image.

Lesson-14.1.8- Transform 2-D shapes by combinations of rotations, reflections and translations.

Chapter-15. Constructions (Geometry)

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Lesson-15.1.1- Construct perpendicular bisectors and angle bisectors. Use a pair of compasses, pencil and ruler.

Lesson-15.1.2- Construct accurate circles, triangles and quadrilaterals using compasses and a ruler.

Lesson-15.1.3- Identify congruent shapes. Use congruent shapes to solve problems about triangles and quadrilaterals. SSS and ASA triangles.

Lesson-15.1.4- Identify two shapes that are similar. Are Shape A and Shape B similar? Explain how you know.

Lesson-15.1.5- Solve problems involving similar triangles. Find the length of the side marked x given another side on this triangle, and the two corresponding sides on the similar triangle.

Chapter-16. Pythagoras’ theorem and trigonometry (Geometry)

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Lesson-16.1.1- Identify and name the hypotenuse, adjacent and opposite of a right-angled triangle.

Lesson-16.1.2- Know and use Pythagoras’ theorem in 2-D. a² + b² = c² Find a missing side given the lengths of the other 2 sides

Lesson-16.1.3- Use trigonometry to calculate lengths and angles in a right-angled triangle. Find a missing side given the length of another side and an angle. Find a missing angle given the length of two sides.

Lesson-16.1.4- Solve problems in context involving right-angled triangles. A ladder reaches 5 m up a wall The bottom of the ladder is 2 m away from the wall. How long is the ladder?

Grade 7 Edexcel Math Achieve Math Excellence

About Lesson

A factory makes 1.21 × 10^7 paper
cups every day.
A cup is made from 1.1 × 10^−2
kilograms of paper.
At the beginning of the day, the
the factory has 1 500 kilograms
of paper.
How much paper will be left at the
end of the day?
Give your answer in standard
form.

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