Exam Skills – Maths Questions 02 November 2019 Exam Skills – Maths Questions Learning outcomes I will be able to: Calculate the mean And give answers to the correct number of significant figures And complete calculations which involve standard form Numeracy Objective Ensure graphs and tables have titles and units. REMEMBER: units are put into brackets. Literacy Objective Correct tense and verb agreement. You must use the correct version of the verb to match the tense. E.g. I see / I saw. I do / I did. Main errors are: We was..... Correct to: We were..... Presentation reminders Underline titles and dates. Include full date annotation. Use a pencil and ruler where appropriate for diagrams and tables. BfL reminders Reminder about phones/headphones given at start of lesson. If phones out after, the teacher will confiscate until the end of the lesson. Maintain a calm, learning environment. No eating, drinking or shouting out.

You add and divide for the mean Averages/Means In science we very rarely use the median or the mode so when we say average we mean.. The MEAN You add and divide for the mean 30 + 10 + 9 + 11 = 60 60 ÷ 4 = 15 15 per minute

You MUST either use brackets (30 + 10 + 9 + 11) ÷ 4 = 15 Averages/Means WARNING: If you type 30 + 10 + 9 + 11 ÷ 4 = 51.75 WRONG A simple check to know if you are probably right… Your answer should be in between the highest and lowest values you added up. 51.75 is not in between 30 and 9 so is definitely wrong 15 is between 30 and 9 so is probably right You MUST either use brackets (30 + 10 + 9 + 11) ÷ 4 = 15 Or do it separately 30 + 10 + 9 + 11 = 60 Then 60 ÷ 4 = 15

Averages/Means WARNING: Do not use anomalous results in your mean calculation. They might warn you about anomalous results (more likely on foundation paper) or they might not (more likely on higher paper) Did you spot the mistake in the example? 10 + 9 + 11 = 30 30 ÷ 3 = 10 10 per minute

Averages/Means

Averages/Means

Averages/Means

Averages/Means

Averages/Means

Averages/Means

Averages/Means

Averages/Means

Significant Figures Did anyone know what to do for this?

Round 17.46789 to 2 significant figures When we round to significant figures, we start counting as soon as we reach a number that is not zero Round 17.46789 to 2 significant figures 1 significant figure 2 significant figures, this will stay a 7 or go to a 8 depending on what the next number is All the numbers after will become zero Round 17.46789 to 2 significant figures= 17.00000 or just 17

It’s more than 4 so we round up! Significant Figures Round to 1 sf 3 7 8 5 4 3 7 Look at the next number It’s more than 4 so we round up!

It’s less than 5 so we round down! Significant Figures Round to 3 sf 3 7 8 4 3 7 Look at the next number It’s less than 5 so we round down!

It’s more than 4 so we round up! Significant Figures Round to 2 sf . 2 9 8 9 Look at the next number It’s more than 4 so we round up!

It’s more than 4 so we round up! Significant Figures Round to 3 sf . 2 8 9 7 Look at the next number It’s more than 4 so we round up!

Significant Figures Round- 0.23 to 1 s.f 0.3 2 A) B) 0.2 3 C) D)

Significant Figures Round- 0.045 to 1 s.f 0.04 0.1 A) B) 0.0 0.05 C) D)

Significant Figures Round- 623 to 1 s.f 600 620 A) B) 630 700 C) D)

Significant Figures Round- 5328 to 1 s.f 5300 5000 A) B) 5330 6000 C) D)

Significant Figures Round- 0.005136 to 2 s.f 0.01 0.0050 A) B) 0.00514 0.0051 C) D)

Significant Figures Round- 426.213 to 2 s.f 426.21 430 A) B) 400.00 420 C) D)

Significant Figures Round- 3002.01 to 3 s.f 300 3000 A) B) 3010 3002.0 C) D)

Significant Figures Round- 983.4 to 1 s.f 100 900 A) B) 980 1000 C) D)

Significant Figures Round- 0.00456 to 2 s.f 0.0045 0.004 A) B) 0.0046 0.00 C) D)

Significant Figures Round- 36345.3 to 3 s.f 36300 4000 A) B) 36000 45300 C) D)

Total to correct sig figs Total to correct sig figs Significant Figures Add the values below then write the answer to the appropriate number of significant figures Value 1 Value 2 Value 3 Total Value Total to correct sig figs 51.4 1.67 3.23   7146 –32.54 12.8 20.8 18.72 0.851 1.4693 10.18 –1.062 9.07 0.56 3.14 739762 26017 2.058 Multiply the values below then write the answer to the appropriate number of significant figures Value 1 Value 2 Total Value Total to correct sig figs 0.91 1.23   8.764 7.63 2.6 31.7 937 40.01 0.722 634.23

For each value state how many significant figures it is stated to. Sig Figs 2.863   689671.49 100000 6.4981 x 107 100 356865 8.5 x 10-3 7.85 24.92 13 6400 17.99 5.18 x 1027 182.15 875.4 3.189 x 106 2.8 4.267 94 0.053 2.9970 0.02 94.0 0.422

What about these values? Standard Form For each value state how many significant figures it is stated to. Value Sig Figs 2.863   689671.49 100000 6.4981 x 107 100 356865 8.5 x 10-3 7.85 24.92 13 6400 17.99 5.18 x 1027 182.15 875.4 3.189 x 106 2.8 4.267 94 0.053 2.9970 0.02 94.0 0.422 What about these values? They are written in standard form

199600000 years ago. Example The Jurassic Age began Standard Form Example The Jurassic Age began 199600000 years ago. Write this in standard form.

199600000 years ago. Example The Jurassic Age began Standard Form Example The Jurassic Age began 199600000 years ago. Write this in standard form. 8 1.996 x 10

Write this in standard form. Question 1 The Earth is 93 000 000 miles from the Sun. Write this in standard form. Ans: 9.3 x 10 miles 7

The average bucket of sand contains 3 180 000 000 grains of sand. Standard Form Question 2 The average bucket of sand contains 3 180 000 000 grains of sand. Write this in standard form. Ans: 3.18 x 10 grains 9

Converting from standard form to normal form Example Anglesey has rock that is 2.6 × 109 years old. Write this number out in full. Ans: 2.6 = 2 600 000 000

Write this in normal form. Standard Form Question 3 Light travels at 3 x 108 m/s Write this in normal form. Ans: 300 000 000 m/s

Worldwide sales of Wii Sports have reached 8.19 x 107 Standard Form Question 4 Worldwide sales of Wii Sports have reached 8.19 x 107 Write this sales figure out in full. Ans: 81 900 000

Standard Form and Calculators If you need to use standard form in a calculations then you will need to be able to type it into your calculator EXAMPLE 3x108 Type 3 x10x 8 Your calculator may be different. You MUST get your own calculator so you can get used to it

Standard Form 1. Convert these numbers into normal form.   a) 5.239 x 103 b) 4.543 x 104 c) 9.382 x 102 d) 6.665 x 106 e) 1.951 x 102 f) 1.905 x 105 g) 6.005 x 103 2. Convert these numbers into standard form. a) 65345 b) 28748 c) 548454 d) 486856 e) 70241 f) 65865758 g) 765 3. Convert these numbers into normal form. a) 8.34  10-3 b) 2.541  10-8 c) 1.01  10-5 d) 8.88  10-1 e) 9  10-2 f) 5.05  10-9 4. Convert these numbers to standard form. a) 0.000567 b) 0.987 c) 0.0052 d) 0.0000605 e) 0.008 f) 0.0040302 Calculate, giving answers in standard form, (3.45  10-5 + 9.5  10-6)  0.0024  (2.31  105  3.98  10-3) + 0.0013

Standard Form

Standard Form Hint: v = f x λ

Standard Form Hint: v = f x λ