Daily Practice · Higher Plus
February 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1958 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1958y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 16.
- 2nd February 1958In a vector proof you find that vector PQ = 5a - 6b and vector RS = 15a - 18b. What does this show about PQ and RS?
- 3rd February 1958A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 4th February 1958On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th February 1958A rectangle is 5 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th February 1958A quadratic sequence starts 15, 33, 59, 93. Work out the second difference, and the coefficient of n^2.
- 7th February 1958A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 8th February 1958A cuboid measures 11 cm by 4 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th February 1958A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th February 1958A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 11th February 1958Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 12th February 1958Solve x^2 - 12x + 20 < 0.
- 13th February 1958y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 14th February 1958A cuboid measures 13 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th February 1958A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th February 1958On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th February 1958A block has mass 690 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th February 1958Write x^2 - 16x - 1 in the form (x + a)^2 + b.
- 19th February 1958y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 20th February 1958The 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.
- 21st February 1958A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 22nd February 1958A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 23rd February 1958x = 188 and y = 40, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th February 1958Work out the coordinates of the turning point of y = x^2 + 12x - 7.
- 25th February 1958y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 4.
- 26th February 1958In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 27th February 1958The probability of winning a game is 4/5. A player expects 104 wins. How many games did they play?
- 28th February 1958On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?