Mathematics Test Revision and Problem Solving

This content covers a variety of math problems including finding maximum perimeter and minimum area of rectangles, determining the largest width of a rectangle, expanding and simplifying algebraic expressions, and analyzing sets of data to find the median, lower quartile, and upper quartile. It also includes factorization and solving equations. The content addresses various mathematical concepts and provides practice problems for enhancement.

• Mathematics
• Test Revision
• Problem Solving
• Algebraic Expressions
• Data Analysis

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1. Test 1 Revision YEAR 9 ENHANCED

2. Write the error interval for the following: Find the maximum perimeter for this rectangle sides measured to 1 d.p. a = 5.3 (1 d.p.) b = 15.7 (3 s.f.) c = 120 (2 s.f.) Find the maximum value of Topic 1 4.3 (1 d.p.) 3.7cm 1.2cm ?? ? 7.26 (2 d.p.) Write the error interval for the following: Find the minimum area for this rectangle sides measured to 1 d.p. a = 5.3 (1 d.p.) b = 15.7 (3 s.f.) c = 120 (2 s.f.) Find the maximum value of Topic 1 246 (3 s.f.) 3.7cm 24 (2 s.f.) 1.2cm ? + ? ? Write the error interval for the following: A rectangle has an area of 25 cm to 2 s.f. It s length is 4.2 cm to 2 s.f.. What is the largest width of the rectangle? a = 5.3 (1 d.p.) b = 15.7 (3 s.f.) c = 120 (2 s.f.) Find the minimum value of Topic 1 340 (2 s.f.) 400 (2 s.f.) ? ? ?

3. Write the error interval for the following: a = 5.3 (1 d.p.) b = 15.7 (3 s.f.) c = 120 (2 s.f.) Find the maximum value of Find the maximum perimeter for this rectangle sides measured to 1 d.p. P = 2(1.25 + 3.75) = 10 Topic 1 4.3 (1 d.p.) 4.25 ? < 4.35 3.7cm 1.2cm ?? ? =5.35 15.75 115 7.26 (2 d.p.) 7.255 ? < 7.265 Write the error interval for the following: a = 5.3 (1 d.p.) b = 15.7 (3 s.f.) c = 120 (2 s.f.) Find the maximum value of Find the minimum area for this rectangle sides measured to 1 d.p. A = 1.15 x 3.65 = 4.1975 Topic 1 246 (3 s.f.) 245.5 ? < 246.5 3.7cm 24 (2 s.f.) 23.5 ? < 24.5 Write the error interval for the following: 1.2cm ? + ? ? a = 5.3 (1 d.p.) b = 15.7 (3 s.f.) c = 120 (2 s.f.) Find the minimum value of =125 + 5.35 15.65 A rectangle has an area of 25 cm to 2 s.f. It s length is 4.2 cm to 2 s.f.. What is the largest width of the rectangle? ? =25.5 4.15= 6.1446 Topic 1 340 (2 s.f.) 335 ? < 345 400 (2 s.f.) 395 ? < 405 ? ? ? =115 5.35 15.75

4. Expand and simplify Factorise Solve 3?2+ 6? ?2+ 11? + 30 = 0 (? + 3)(? 4) Topic 2 ?2+ 7? + 12 Expand and simplify Factorise Solve ?2 6? 16 ?2+ 4? 21 = 0 (2? + 5)(3? 1) Topic 2 ?2 7? + 12 Expand and simplify Factorise Solve (4? 5?)(3? 2?) ?2 25 ?2 9? + 20 = 0 Topic 2 9?2 49

5. Expand and simplify Factorise Solve 3?2+ 6? = 3?(? + 2) ?2+ 7? + 12 = (? + 3)(? + 4) ?2+ 11? + 30 = 0 ? + 5 ? + 6 = 0 (? + 3)(? 4) = ?2 ? 12 Topic 2 ? = 5 ?? ? = 6 Expand and simplify Factorise Solve ?2 6? 16 = (? + 2)(? 8) ?2+ 4? 21 = 0 ? + 7 ? 3 = 0 2? + 5 3? 1 = 6?2+ 13? 5 Topic 2 ?2 7? + 12 = (? 3)(? 4) ? = 7 ?? ? = 3 Expand and simplify Factorise Solve (4? 5?)(3? 2?) = 12?2 23?? 10?2 ?2 25 = (? + 5)(? 5) ?2 9? + 20 = 0 ? 4 ? 5 = 0 Topic 2 9?2 49 = (3? + 7)(3? 7) ? = 4 ?? ? = 5

6. Find the median, lower quartile and upper quartile for this set of data: Find the median, lower quartile and upper quartile for this set of data: Find the median, lower quartile and upper quartile for this set of data: Topic 3 1, 3, 6, 10, 12, 13, 15 6, 11, 12, 13, 15, 15, 20 ,24 1, 3, 6, 9, 12, 17, 19, 21, 22 ,24 Find the upper quartile: Find the maximum Min LQ Median IQR Range Find the lower quartile: Find the minimum Median IQR UQ Maximum Range The box plot displays the heights of 80 plants. How many plants were shorter than 18 cm? 32 15 40 45 35 4 8 Topic 3 10 9 16 0 5 10 15 20 25cm Complete the cumulative frequency table Time Freq 0-10 7 10-20 8 20-30 5 30-40 3 80 Cumulative frequency Find the inter quartile range. 60 C F Topic 3 40 How many items weighed more than 20 kg? 20 0 10 20 30 Weight kg

7. Find the median, lower quartile and upper quartile for this set of data: 1, 3, 6, 10, 12, 13, 15 Find the median, lower quartile and upper quartile for this set of data: 1, 3, 6, 9, 12, 17, 19, 21, 22 ,24 Find the median, lower quartile and upper quartile for this set of data: Topic 3 6, 11, 12, 13, 15, 15, 20 ,24 Median = 14 LQ = 11.5 UQ = 17.5 Median = 14.5 LQ = 6 UQ = 21 Median = 10 LQ = 3 UQ =13 Find the upper quartile: Find the maximum Min LQ Median IQR Range Find the lower quartile: Find the minimum Median IQR UQ Maximum Range The box plot displays the heights of 80 plants. How many plants were shorter than 18 cm? of 80 = 60 UQ = 8 + 9 = 17 Max = 4 + 16 = 20 LQ = 40 - 15 = 25 Min = 45 - 35 = 10 4 8 32 15 40 45 35 Topic 3 10 9 16 0 5 10 15 20 25cm Complete the cumulative frequency table Time Freq 0-10 7 10-20 8 20-30 5 30-40 3 80 Cumulative frequency Find the inter quartile range. 24 18 = 6 How many items weighed more than 20 kg? 80 32 = 48 60 C F 7 15 20 23 Topic 3 40 20 0 10 20 30 Weight kg

8. Calculate the speed if Write in standard form: Write in standard form: 42000000 35 x 105 D = 6 x 105 Topic 4 T = 2 x 102 0.00065 0.4 x 10-3 Calculate: Calculate: Write in normal notation 3.5 x 106 4.1 x 104 + 5 x 105 4 x 104 x 2 x 103 Topic 4 5.1 x 10-1 3.7 x 10-1 - 2 x 10-2 9.6 x 105 3 x 10-2 Evaluate Evaluate Evaluate 70 3 2 1 2 Topic 4 36 5 3 25 0 2 3 27

9. Calculate the speed if Write in standard form: Write in standard form: 42000000 = 4.2 x 107 0.00065 = 6.5 x 10-4 35 x 105 = 3.5 x 106 0.4 x 10-3 = 4 x 10-4 D = 6 x 105 Topic 4 T = 2 x 102 = 3 x 103 Calculate: Calculate: Write in normal notation 3.5 x 106 = 3 500 000 5.1 x 10-1 = 0.51 4.1 x 104 + 5 x 105 = 5.41 x 105 3.7 x 10-1 - 2 x 10-2 = 3.5 x 10-1 4 x 104 x 2 x 103 = 8 x 107 9.6 x 105 3 x 10-2 = 3.2 x 107 Topic 4 Evaluate Evaluate Evaluate 70 = 1 1 2= 6 3 2=1 Topic 4 36 9 25 0 = 1 2 3= 9 1 27 5 3= 125