Daily Practice · Higher Plus
June 1994 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1994 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1994
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1994A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 2nd June 1994Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
- 3rd June 1994Solve x^2 + 13x + 42 > 0.
- 4th June 1994y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 5th June 1994A cuboid measures 12 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th June 1994A bag holds 3 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th June 1994On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th June 1994A rectangle is 6 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th June 1994Write x^2 - 8x + 6 in the form (x + a)^2 + b.
- 10th June 1994A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 11th June 1994The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 12th June 1994A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 13th June 1994A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 14th June 1994Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 15th June 1994Work out the coordinates of the turning point of y = x^2 - 8x + 1.
- 16th June 1994y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 17th June 1994In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 18th June 1994The probability of winning a game is 4/5. A player expects 8 wins. How many games did they play?
- 19th June 1994On 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?
- 20th June 1994A block has mass 660 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st June 1994Simplify (x^2 - 9x + 18)/(x - 3).
- 22nd June 1994y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 23rd June 1994In a vector proof you find that vector PQ = 3a - 5b and vector RS = 9a - 15b. What does this show about PQ and RS?
- 24th June 1994A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 25th June 1994A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 26th June 1994x = 46 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th June 1994In an algebraic proof, how would you write a multiple of 6 in terms of an integer n?
- 28th June 1994y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 4.
- 29th June 1994A cuboid measures 9 cm by 14 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th June 1994A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?