Daily Practice · Higher Plus
January 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1958 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1958Use the iteration x(n+1) = cube root of (2x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 2nd January 1958y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 3rd January 1958In a vector proof you find that vector PQ = a + b and vector RS = 3a + 3b. What does this show about PQ and RS?
- 4th January 1958A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 5th January 1958A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 6th January 1958A block has mass 510 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.
- 7th January 1958Work out the nth term of the quadratic sequence 5, 13, 27, 47, ...
- 8th January 1958y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 4.
- 9th January 1958A cuboid measures 9 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th January 1958A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th January 1958On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th January 1958x = 50 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th January 1958The point (2, 1) lies on y = f(x). Write down its image on y = f(x - 1).
- 14th January 1958A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 15th January 1958A cuboid measures 14 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th January 1958A bag holds 6 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th January 1958A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 18th January 1958A car covers 130 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.
- 19th January 1958Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 20th January 1958y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 21st January 1958The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 22nd January 1958A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 23rd January 1958On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th January 1958Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 25th January 1958f(x) = 5x - 7 and g(x) = 4x + 2. Work out fg(4).
- 26th January 1958y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 27th January 1958In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 28th January 1958The probability of winning a game is 5/8. A player expects 35 wins. How many games did they play?
- 29th January 1958A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 30th January 1958Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 31st January 1958The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.