Review Think mathematics 1A ( chapter 1- 4)

-

Mathematical Summary

Mathematical Theories and Formulas

1. Highest Common Factor (HCF) and Lowest Common Multiple (LCM)

HCF: The greatest number that divides two or more numbers without a remainder. Use prime factorization and take the lowest power of all common prime factors.

LCM: The smallest number that is a multiple of two or more numbers. Use prime factorization and take the highest power of all prime factors.

2. Prime Factorization

Express numbers as products of their prime factors, e.g., \( n = 2^a \times 3^b \times 5^c \).

3. Arithmetic and Algebraic Operations

  • Basic operations: addition, subtraction, multiplication, division.
  • Simplify algebraic expressions using identities and operations.

4. Estimation Techniques

Round numbers to simplify calculations, e.g., estimating products and square roots.

5. Evaluating Expressions

  • Substitute values into expressions and simplify.
  • Use logical reasoning to find solutions.

6. Geometry and Measurement

Calculate areas and volumes, e.g., area of a rectangle is \( \text{length} \times \text{width} \).

7. Financial Calculations

Calculate total costs, e.g., finding the cost of multiple items in dollars.

8. Temperature and Change

Calculate changes in temperature over time, e.g., overall change from midnight to 6 p.m.

9. Problem-Solving Strategies

  • Identify the problem and relevant information.
  • Apply appropriate mathematical techniques to solve.

10. Simplification and Factorization

Simplify expressions and factorize algebraic equations, e.g., using common factors and identities.

11. Fractions and Decimals

Perform operations with fractions and decimals, including simplification and conversion.


Practice

  1. List
    (a) the composite numbers,
    (b) the perfect cubes.

    1, 2, 16, 33, 49, 511, 1000

  2. (a) Calculate $$\frac{(-14.8)^{2}}{23.56 \times 0.979}$$.
    Write down the first five digits on your calculator display.

    (b) Write your answer to part (a) correct to 3 significant figures.

  3. Without using a calculator, find the value of $$5-\frac{2}{3} \times \frac{7}{8} \div\left(-\frac{1}{2}\right)^{2}$$.

  4. Expand and simplify $$5[5 x-2 y(4 x-3)+6 y]-10 x$$.

  5. A straight line is drawn passing through the points $$(-3,0)$$ and $$(5,-4)$$.
    Find the gradient of the line.

  6. (a) Factorise $$12 a b c-28 a b c x+36 a c x$$ completely.

    (b) Without using a calculator, find the value of $$169 \times 1003-3 \times 169$$.

  7. It is given that $$\frac{5 x+y}{7 x-3 y}=\frac{1}{2}$$.
    Find the value of $$\frac{y}{x}$$.

  8. Solve $$\frac{3 x+7}{2}-1=\frac{2 x}{3}$$.

  9. (a) Give two examples of irrational numbers.

    (b) Express $$0 . \dot{3} \dot{9}$$ in the form $$\frac{a}{b}$$, where $$a$$ and $$b$$ are integers and $$b \neq 0$$.

  10. A plot of land is used to grow flowers.
    $$\frac{1}{5}$$ of the land is allocated for orchids.
    After the orchids have been planted, $$\frac{2}{3}$$ of the remaining land is allocated for roses.
    After orchids and roses have been planted, 0.75 of the remaining land is allocated for tulips.
    What fraction of the plot of land is not occupied by the flowers?

Show All Answers

Popular posts from this blog

Aljabar kelas 7

-
Image
Aljabar: Konsep Dasar dan Operasi 1. Bentuk Aljabar Bentuk aljabar adalah ekspresi matematika yang terdiri dari variabel, konstanta, dan operasi matematika. Contoh: 3x + 2y - 7 Komponen Bentuk Aljabar: Variabel: Huruf yang mewakili nilai yang tidak diketahui (x, y, z) Koefisien: Angka yang mengalikan variabel (3 dalam 3x) Konstanta: Angka tanpa variabel (-7 dalam contoh di atas) Suku: Bagian dari bentuk aljabar yang dipisahkan oleh operasi penjumlahan atau pengurangan 2. Operasi Aljabar a. Penjumlahan dan Pengurangan Hanya suku-suku sejenis yang dapat dijumlahkan atau dikurangkan. Contoh: (3x + 2y) + (5x - 3y) = 8x - y b. Perkalian Gunakan sifat distributif untuk mengalikan bentuk aljabar. Contoh: (x + 3)(x + 7) = x² + 10x + 21 c. Pembagian Pembagian bentuk aljabar dapat dilakukan dengan memfaktorkan pembilang dan penyebut. Contoh: (x² - 4) ÷ (x - 2) = x + 2 3. Pemfaktoran Pemfaktoran adalah proses menguraikan bentuk aljabar menjadi
Read more

Aljabar kelas 7A

-
Image
Konsep Dasar dan Operasi Aljabar Panduan Lengkap untuk Pemahaman Aljabar 1. Pengertian dan Komponen Aljabar Komponen Utama Aljabar: Variabel (x, y, z) Koefisien (angka di depan variabel) Konstanta (angka tanpa variabel) Suku (term) Contoh Bentuk Aljabar: 3x² + 4x - 5 3x² 4x -5 2. Operasi Dasar Aljabar a. Penjumlahan dan Pengurangan Aturan Dasar: Hanya suku sejenis yang dapat dijumlahkan/dikurangkan Perhatikan tanda positif dan negatif Contoh: (5x² + 3x - 2) + (2x² - 4x + 1) = 7x² - x - 1 b. Perkalian Aljabar Rumus-rumus Penting: (a + b)² = a² + 2ab + b² (a - b)² = a² - 2ab + b² (a + b)(a - b) = a² - b² Visualisasi (a + b)² a² ab ab b² 3. Pemfaktoran Metode Pemfaktoran: Faktor Persekutuan Terbesar (FPB) 6x² + 12x = 6x(x + 2) Selisih Kuadrat x² - 25 = (x + 5)(x - 5) Kua
Read more

Coordinate Geometry AS & A level

-
Image
Coordinate Geometry Coordinate Geometry 1. Midpoint and Length of a Line Segment The midpoint \(M\) of a line segment joining points \(P(x_1, y_1)\) and \(Q(x_2, y_2)\) is given by: \( M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \) The length of the line segment \(PQ\) is: \( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) 2. Gradient of a Line The gradient (slope) of the line joining the points \(P(x_1, y_1)\) and \(Q(x_2, y_2)\) is: \( \frac{y_2 - y_1}{x_2 - x_1} \) 3. Parallel and Perpendicular Lines For parallel lines, the gradients \(m_1\) and \(m_2\) are equal: \( m_1 = m_2 \) For perpendicular lines, the product of their gradients is: \( m_1 \times m_2 = -1 \) 4. Equation of a Straight Line The equation of a straight line with gradient \(m\) passing through point \((x_1, y_1)\) is: \( y - y_1
Read more