Daily Practice · Higher Plus
February 1957 5-a-day
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The batch download puts all 5 tiers' February 1957 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1957In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 2nd February 1957The probability of winning a game is 1/5. A player expects 13 wins. How many games did they play?
- 3rd February 1957A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 4th February 1957A block has mass 540 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th February 1957Write 5/(x + 1) + 6/(x + 2) as a single fraction.
- 6th February 1957y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 25.
- 7th February 1957In a vector proof you find that vector PQ = 2a + b and vector RS = 4a + 2b. What does this show about PQ and RS?
- 8th February 1957A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 9th February 1957On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th February 1957x = 47 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th February 1957Solve 3x^2 + 23x + 30 = 0.
- 12th February 1957A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 13th February 1957A cuboid measures 12 cm by 13 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th February 1957A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th February 1957A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 16th February 1957A car covers 710 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th February 1957f(x) = 7x - 9. Work out the inverse function f^-1(x).
- 18th February 1957y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 19th February 1957A cuboid measures 12 cm by 4 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th February 1957A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st February 1957On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd February 1957Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 23rd February 1957Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 24th February 1957y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 25th February 1957The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 26th February 1957A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 27th February 1957A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 28th February 1957Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).