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GCSE Maths Higher Tier Practice PDF (Free + Answered)

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GCSE Maths Higher Tier Practice PDF (Free + Answered)

Maths

10/11

Past Paper

This GCSE higher tier maths practice exam PDF covers a wide range of mathematical concepts and problem-solving skills. It contains 23 pages of questions on topics like algebra, geometry, probability, and more. The exam is designed to test students' understanding and application of key mathematical principles in preparation for the actual GCSE Maths exam.

Highlight: This practice exam provides excellent preparation for students taking the GCSE Maths past papers PDF with answers.

Key features of this practice exam include:

80 total marks
90 minute time limit
Calculator allowed
Mix of short and extended response questions
Emphasis on showing all working out
Questions increase in difficulty throughout

Vocabulary: Higher tier - The more advanced level of GCSE Maths exams, covering more complex topics than the Foundation tier.

This resource is ideal for students looking for GCSE higher tier maths practice exam free materials to supplement their studies. It closely mimics the format and style of questions found on actual GCSE Maths past papers with answers.

26/10/2023

2370

Page 1: Exam Overview

The first page provides key information about the GCSE higher tier maths practice exam. It outlines that this is a mock exam from January 2022 for Maths Paper 2 (Higher tier) with calculator allowed. The page lists required materials including blue/black pen, ruler, protractor, pencil and eraser. Instructions state that all questions should be answered in the spaces provided and all working out must be shown. The total mark for the paper is 80 and the time allowed is 90 minutes.

Highlight: This practice exam closely mirrors the format of actual GCSE Maths past papers PDF with answers, providing authentic exam preparation.

GCSE Mock Exam (Jan 2022)
Maths 2 (Higher) - Calc
Materials
Use a blue/black pen.
You must have a ruler, protractor, pencil and eraser. Trac

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Page 2: Algebra and Equations

This page focuses on algebraic manipulation and equation solving, key skills for the GCSE higher tier maths practice exam. Question 1 asks students to simplify algebraic expressions and solve an inequality. Part (a) requires simplification of 14y/3, part (b) involves simplifying p^t × p^(-t), and part (c) asks to solve the inequality 7y > 9 × 3.

Example: For part (b), students need to apply the laws of exponents to simplify p^t × p^(-t) to 1.

Vocabulary: Simplify - To reduce an expression to its simplest form by combining like terms or cancelling out factors.

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Page 3: Speed, Distance, and Time

This page presents a problem involving speed, distance, and time calculations, a common topic in GCSE Maths past papers with answers. Question 2 describes Andrea's journey, which consists of driving 110 km at 40 km/h and then running 14 km at 8 km/h. Students must calculate the total time taken for both parts of the journey, giving the answer in hours and minutes.

Example: To solve this, students should:

Calculate time for driving: 110 km ÷ 40 km/h = 2.75 hours

Calculate time for running: 14 km ÷ 8 km/h = 1.75 hours

Add the times: 2.75 + 1.75 = 4.5 hours

Convert to hours and minutes: 4 hours 30 minutes

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Page 4: Transformations

This page focuses on geometric transformations, a key topic in the GCSE higher tier maths practice exam 2020 and other years. Question 3(a) requires students to translate shape P by the vector (-9, 5). The question provides a coordinate grid with shape P already drawn.

Definition: Translation - A transformation that moves every point of a shape the same distance in the same direction.

Highlight: Understanding transformations is crucial for success in the geometry sections of GCSE Maths past papers Foundation and Higher tiers.

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Page 5: Transformations (continued)

This page continues with transformations, asking students to describe a single transformation that maps shape A onto shape B. The correct answer is a reflection in the line y = x. This type of question is common in GCSE Maths past papers PDF with answers AQA and other exam boards.

Vocabulary: Reflection - A transformation that flips a shape over a line, creating a mirror image.

Highlight: Being able to identify and describe transformations is a key skill tested in GCSE Maths past papers Foundation and Higher tiers.

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Page 6: Compound and Simple Interest

This page presents a problem comparing compound and simple interest, a topic frequently appearing in GCSE higher tier maths practice exam free resources. Question 4 describes two investments of £4000 over 3 years, one with compound interest at 1.8% per year and one with simple interest at the same rate. Students must calculate how much more interest the compound interest investment earns.

Definition:

Compound Interest: Interest calculated on the initial principal and the accumulated interest from previous periods.

Simple Interest: Interest calculated only on the principal amount.

Example: For compound interest: £4000 × (1.018)³ = £4219.91 For simple interest: £4000 + (£4000 × 0.018 × 3) = £4216.00 Difference: £4219.91 - £4216.00 = £3.91

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Page 7: Rounding and Trigonometry

This page covers two distinct topics: rounding and trigonometry, both common in GCSE Maths past papers with answers. Question 5 asks students to complete a statement about the range of possible values for a height given as 184 meters to the nearest meter. Question 6 involves using trigonometry to calculate the perimeter of a rectangle given one side length and an angle.

Vocabulary: Significant figures - The digits in a number that carry meaning contributing to its precision.

Example: For Question 6, students need to use tan(35°) = opposite/adjacent to find the unknown side length, then add all sides to find the perimeter.

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Page 8: Mean Calculations and Ratio

This page focuses on calculating means and working with ratios, essential skills for the GCSE higher tier maths practice exam. Question 7 requires students to calculate the overall mean age of an orchestra given the mean ages and numbers of men and women separately. Question 8 asks students to prove a relationship between ratios.

Definition: Mean - The average of a set of numbers, calculated by summing all values and dividing by the count of values.

Highlight: Questions involving means and ratios are common in GCSE Maths past papers Foundation and Higher tiers, often requiring multi-step solutions.

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Page 9: Probability

This page presents a probability problem, a topic frequently tested in GCSE Maths past papers PDF with answers. Question 9 describes a bag of colored counters and provides some probability information. Students must use this information to calculate the number of red counters in the bag.

Vocabulary: Probability - The likelihood of an event occurring, expressed as a number between 0 and 1.

Example: To solve this, students need to:

Find the probability of yellow counters

Use this to find the probability of red counters

Calculate the number of red counters out of 500 total

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Page 10: Percentage Increase and Algebra

This page covers percentage increase calculations and algebraic expansion, both key topics in GCSE higher tier maths practice exam free resources. Question 10 involves working backwards from a house value after two years of 1.5% annual increases to find the original value. Question 11 asks students to expand and simplify a product of three linear expressions.

Highlight: These types of multi-step problems are common in GCSE Maths past papers with answers, testing students' ability to apply multiple concepts.

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Page 11: Solving Equations

This page focuses on solving a complex equation, a skill frequently tested in GCSE Maths past papers PDF with answers AQA and other exam boards. Question 12 requires students to solve the equation (8-3x)/4 = 8-2x. This involves algebraic manipulation and fraction operations.

Example: To solve this equation, students should:

Multiply both sides by 4 to eliminate fractions

Expand brackets

Collect like terms

Isolate the variable

Highlight: Equation solving is a fundamental skill assessed in all GCSE Maths past papers Foundation and Higher tiers.

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Page 12: Combinations

This page deals with combinations, a topic in probability and statistics that appears in many GCSE higher tier maths practice exam 2020 papers and other years. Question 13 asks students to calculate the number of ways to choose students for a competition from a class of boys and girls.

Vocabulary: Combinations - The number of ways to select items from a collection where order doesn't matter.

Example: For part (a), students multiply 16 (number of girls) by 14 (number of boys) to get 224 ways to choose one of each.

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Page 13: Equation Solving and Iteration

This final page focuses on advanced equation solving techniques, including graphical methods and iteration. These topics are key components of the GCSE higher tier maths practice exam. Question 14 asks students to show that an equation has a solution between two values, rearrange the equation, and use an iteration formula.

Definition: Iteration - A problem-solving method that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems.

Highlight: These advanced algebra skills are crucial for success in the higher tier GCSE Maths past papers with answers.

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